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Título : Mathematical Problems in Image Processing : Partial Differential Equations and the Calculus of Variations Tipo de documento: documento electrónico Autores: Gilles Aubert ; SpringerLink (Online service) ; Pierre Kornprobst Editorial: New York, NY : Springer New York Fecha de publicación: 2006 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 147 Número de páginas: XXXI, 379 p Il.: online resource ISBN/ISSN/DL: 978-0-387-44588-5 Idioma : Inglés (eng) Palabras clave: Mathematics Image processing Mathematical analysis Analysis (Mathematics) Partial differential equations Optics Optoelectronics Plasmons (Physics) Applied mathematics Engineering Optics, Optoelectronics, Plasmonics and Optical Devices Appl.Mathematics/Computational Methods of Differential Equations Processing Computer Vision Signal, Speech Clasificación: 51 Matemáticas Resumen: Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago. Since then, intensive research has been carried out. The goals of this book are to present a variety of image analysis applications, the precise mathematics involved and how to discretize them. Thus, this book is intended for two audiences. The first is the mathematical community by showing the contribution of mathematics to this domain. It is also the occasion to highlight some unsolved theoretical questions. The second is the computer vision community by presenting a clear, self-contained and global overview of the mathematics involved in image processing problems. This work will serve as a useful source of reference and inspiration for fellow researchers in Applied Mathematics and Computer Vision, as well as being a basis for advanced courses within these fields. During the four years since the publication of the first edition, there has been substantial progress in the range of image processing applications covered by the PDE framework. The main goals of the second edition are to update the first edition by giving a coherent account of some of the recent challenging applications, and to update the existing material. In addition, this book provides the reader with the opportunity to make his own simulations with a minimal effort. To this end, programming tools are made available, which will allow the reader to implement and test easily some classical approaches. Reviews of the earlier edition: "Mathematical Problems in Image Processing is a major, elegant, and unique contribution to the applied mathematics literature, oriented toward applications in image processing and computer vision.... Researchers and practitioners working in the field will benefit by adding this book to their personal collection. Students and instructors will benefit by using this book as a graduate course textbook." -- SIAM Review "The Mathematician -- and he doesn't need to be a 'die-hard' applied mathematician -- will love it because there are all these spectacular applications of nontrivial mathematical techniques and he can even find some open theoretical questions. The numerical analyst will discover many challenging problems and implementations. The image processor will be an eager reader because the book provides all the mathematical elements, including most of the proofs.... Both content and typography are a delight. I can recommend the book warmly for theoretical and applied researchers." -- Bulletin of the Belgian Mathematics Nota de contenido: Foreword -- Preface to the Second Edition -- Preface -- Guide to the Main Mathematical Concepts and their Application -- Notation and Symbols -- Introduction -- Mathematical Preliminaries -- Image Restoration -- The Segmentation Problem -- Other Challenging Applications -- A Introduction to Finite Difference Methods -- B Experiment Yourself!- References -- Index En línea: http://dx.doi.org/10.1007/978-0-387-44588-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34844 Mathematical Problems in Image Processing : Partial Differential Equations and the Calculus of Variations [documento electrónico] / Gilles Aubert ; SpringerLink (Online service) ; Pierre Kornprobst . - New York, NY : Springer New York, 2006 . - XXXI, 379 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 147) .
ISBN : 978-0-387-44588-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Image processing Mathematical analysis Analysis (Mathematics) Partial differential equations Optics Optoelectronics Plasmons (Physics) Applied mathematics Engineering Optics, Optoelectronics, Plasmonics and Optical Devices Appl.Mathematics/Computational Methods of Differential Equations Processing Computer Vision Signal, Speech Clasificación: 51 Matemáticas Resumen: Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago. Since then, intensive research has been carried out. The goals of this book are to present a variety of image analysis applications, the precise mathematics involved and how to discretize them. Thus, this book is intended for two audiences. The first is the mathematical community by showing the contribution of mathematics to this domain. It is also the occasion to highlight some unsolved theoretical questions. The second is the computer vision community by presenting a clear, self-contained and global overview of the mathematics involved in image processing problems. This work will serve as a useful source of reference and inspiration for fellow researchers in Applied Mathematics and Computer Vision, as well as being a basis for advanced courses within these fields. During the four years since the publication of the first edition, there has been substantial progress in the range of image processing applications covered by the PDE framework. The main goals of the second edition are to update the first edition by giving a coherent account of some of the recent challenging applications, and to update the existing material. In addition, this book provides the reader with the opportunity to make his own simulations with a minimal effort. To this end, programming tools are made available, which will allow the reader to implement and test easily some classical approaches. Reviews of the earlier edition: "Mathematical Problems in Image Processing is a major, elegant, and unique contribution to the applied mathematics literature, oriented toward applications in image processing and computer vision.... Researchers and practitioners working in the field will benefit by adding this book to their personal collection. Students and instructors will benefit by using this book as a graduate course textbook." -- SIAM Review "The Mathematician -- and he doesn't need to be a 'die-hard' applied mathematician -- will love it because there are all these spectacular applications of nontrivial mathematical techniques and he can even find some open theoretical questions. The numerical analyst will discover many challenging problems and implementations. The image processor will be an eager reader because the book provides all the mathematical elements, including most of the proofs.... Both content and typography are a delight. I can recommend the book warmly for theoretical and applied researchers." -- Bulletin of the Belgian Mathematics Nota de contenido: Foreword -- Preface to the Second Edition -- Preface -- Guide to the Main Mathematical Concepts and their Application -- Notation and Symbols -- Introduction -- Mathematical Preliminaries -- Image Restoration -- The Segmentation Problem -- Other Challenging Applications -- A Introduction to Finite Difference Methods -- B Experiment Yourself!- References -- Index En línea: http://dx.doi.org/10.1007/978-0-387-44588-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34844 Ejemplares
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Título : Around the Research of Vladimir Maz'ya II : Partial Differential Equations Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Ari Laptev Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Otro editor: Imprint: Springer Colección: International Mathematical Series, ISSN 1571-5485 num. 12 Número de páginas: XXII, 386 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-1343-2 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: International Mathematical Series Volume 12 Around the Research of Vladimir Maz'ya II Partial Differential Equations Edited by Ari Laptev Numerous influential contributions of Vladimir Maz'ya to PDEs are related to diverse areas. In particular, the following topics, close to the scientific interests of V. Maz'ya are discussed: semilinear elliptic equation with an exponential nonlinearity resolvents, eigenvalues, and eigenfunctions of elliptic operators in perturbed domains, homogenization, asymptotics for the Laplace-Dirichlet equation in a perturbed polygonal domain, the Navier-Stokes equation on Lipschitz domains in Riemannian manifolds, nondegenerate quasilinear subelliptic equations of p-Laplacian type, singular perturbations of elliptic systems, elliptic inequalities on Riemannian manifolds, polynomial solutions to the Dirichlet problem, the first Neumann eigenvalues for a conformal class of Riemannian metrics, the boundary regularity for quasilinear equations, the problem on a steady flow over a two-dimensional obstacle, the well posedness and asymptotics for the Stokes equation, integral equations for harmonic single layer potential in domains with cusps, the Stokes equations in a convex polyhedron, periodic scattering problems, the Neumann problem for 4th order differential operators. Contributors include: Catherine Bandle (Switzerland), Vitaly Moroz (UK), and Wolfgang Reichel (Germany); Gerassimos Barbatis (Greece), Victor I. Burenkov (Italy), and Pier Domenico Lamberti (Italy); Grigori Chechkin (Russia); Monique Dauge (France), Sebastien Tordeux (France), and Gregory Vial (France); Martin Dindos (UK); Andras Domokos (USA) and Juan J. Manfredi (USA); Yuri V. Egorov (France), Nicolas Meunier (France), and Evariste Sanchez-Palencia (France); Alexander Grigor'yan (Germany) and Vladimir A. Kondratiev (Russia); Dmitry Khavinson (USA) and Nikos Stylianopoulos (Cyprus); Gerasim Kokarev (UK) and Nikolai Nadirashvili (France); Vitali Liskevich (UK) and Igor I. Skrypnik (Ukraine); Oleg Motygin (Russia) and Nikolay Kuznetsov (Russia); Grigory P. Panasenko (France) and Ruxandra Stavre (Romania); Sergei V. Poborchi (Russia); Jurgen Rossmann (Germany); Gunther Schmidt (Germany); Gregory C. Verchota (USA). Ari Laptev Imperial College London (UK) and Royal Institute of Technology (Sweden) Ari Laptev is a world-recognized specialist in Spectral Theory of Differential Operators. He is the President of the European Mathematical Society for the period 2007- 2010. Tamara Rozhkovskaya Sobolev Institute of Mathematics SB RAS (Russia) and an independent publisher Editors and Authors are exclusively invited to contribute to volumes highlighting recent advances in various fields of mathematics by the Series Editor and a founder of the IMS Tamara Rozhkovskaya. Cover image: Vladimir Maz'ya Nota de contenido: Large Solutions to Semilinear Elliptic Equations with Hardy Potential and Exponential Nonlinearity -- Stability Estimates for Resolvents, Eigenvalues, and Eigenfunctions of Elliptic Operators on Variable Domains -- Operator Pencil in a Domain with Concentrated Masses. A Scalar Analog of Linear Hydrodynamics -- Selfsimilar Perturbation near a Corner: Matching Versus Multiscale Expansions for a Model Problem -- Stationary Navier#x2013;Stokes Equation on Lipschitz Domains in Riemannian Manifolds with Nonvanishing Boundary Conditions -- On the Regularity of Nonlinear Subelliptic Equations -- Rigorous and Heuristic Treatment of Sensitive Singular Perturbations Arising in Elliptic Shells -- On the Existence of Positive Solutions of Semilinear Elliptic Inequalities on Riemannian Manifolds -- Recurrence Relations for Orthogonal Polynomials and Algebraicity of Solutions of the Dirichlet Problem -- On First Neumann Eigenvalue Bounds for Conformal Metrics -- Necessary Condition for the Regularity of a Boundary Point for Porous Medium Equations with Coefficients of Kato Class -- The Problem of Steady Flow over a Two-Dimensional Bottom Obstacle -- Well Posedness and Asymptotic Expansion of Solution of Stokes Equation Set in a Thin Cylindrical Elastic Tube -- On Solvability of Integral Equations for Harmonic Single Layer Potential on the Boundary of a Domain with Cusp -- H#x00F6;lder Estimates for Green#x2019;s Matrix of the Stokes System in Convex Polyhedra -- Boundary Integral Methods for Periodic Scattering Problems -- Boundary Coerciveness and the Neumann Problem for 4th Order Linear Partial Differential Operators En línea: http://dx.doi.org/10.1007/978-1-4419-1343-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33592 Around the Research of Vladimir Maz'ya II : Partial Differential Equations [documento electrónico] / SpringerLink (Online service) ; Ari Laptev . - New York, NY : Springer New York : Imprint: Springer, 2010 . - XXII, 386 p : online resource. - (International Mathematical Series, ISSN 1571-5485; 12) .
ISBN : 978-1-4419-1343-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: International Mathematical Series Volume 12 Around the Research of Vladimir Maz'ya II Partial Differential Equations Edited by Ari Laptev Numerous influential contributions of Vladimir Maz'ya to PDEs are related to diverse areas. In particular, the following topics, close to the scientific interests of V. Maz'ya are discussed: semilinear elliptic equation with an exponential nonlinearity resolvents, eigenvalues, and eigenfunctions of elliptic operators in perturbed domains, homogenization, asymptotics for the Laplace-Dirichlet equation in a perturbed polygonal domain, the Navier-Stokes equation on Lipschitz domains in Riemannian manifolds, nondegenerate quasilinear subelliptic equations of p-Laplacian type, singular perturbations of elliptic systems, elliptic inequalities on Riemannian manifolds, polynomial solutions to the Dirichlet problem, the first Neumann eigenvalues for a conformal class of Riemannian metrics, the boundary regularity for quasilinear equations, the problem on a steady flow over a two-dimensional obstacle, the well posedness and asymptotics for the Stokes equation, integral equations for harmonic single layer potential in domains with cusps, the Stokes equations in a convex polyhedron, periodic scattering problems, the Neumann problem for 4th order differential operators. Contributors include: Catherine Bandle (Switzerland), Vitaly Moroz (UK), and Wolfgang Reichel (Germany); Gerassimos Barbatis (Greece), Victor I. Burenkov (Italy), and Pier Domenico Lamberti (Italy); Grigori Chechkin (Russia); Monique Dauge (France), Sebastien Tordeux (France), and Gregory Vial (France); Martin Dindos (UK); Andras Domokos (USA) and Juan J. Manfredi (USA); Yuri V. Egorov (France), Nicolas Meunier (France), and Evariste Sanchez-Palencia (France); Alexander Grigor'yan (Germany) and Vladimir A. Kondratiev (Russia); Dmitry Khavinson (USA) and Nikos Stylianopoulos (Cyprus); Gerasim Kokarev (UK) and Nikolai Nadirashvili (France); Vitali Liskevich (UK) and Igor I. Skrypnik (Ukraine); Oleg Motygin (Russia) and Nikolay Kuznetsov (Russia); Grigory P. Panasenko (France) and Ruxandra Stavre (Romania); Sergei V. Poborchi (Russia); Jurgen Rossmann (Germany); Gunther Schmidt (Germany); Gregory C. Verchota (USA). Ari Laptev Imperial College London (UK) and Royal Institute of Technology (Sweden) Ari Laptev is a world-recognized specialist in Spectral Theory of Differential Operators. He is the President of the European Mathematical Society for the period 2007- 2010. Tamara Rozhkovskaya Sobolev Institute of Mathematics SB RAS (Russia) and an independent publisher Editors and Authors are exclusively invited to contribute to volumes highlighting recent advances in various fields of mathematics by the Series Editor and a founder of the IMS Tamara Rozhkovskaya. Cover image: Vladimir Maz'ya Nota de contenido: Large Solutions to Semilinear Elliptic Equations with Hardy Potential and Exponential Nonlinearity -- Stability Estimates for Resolvents, Eigenvalues, and Eigenfunctions of Elliptic Operators on Variable Domains -- Operator Pencil in a Domain with Concentrated Masses. A Scalar Analog of Linear Hydrodynamics -- Selfsimilar Perturbation near a Corner: Matching Versus Multiscale Expansions for a Model Problem -- Stationary Navier#x2013;Stokes Equation on Lipschitz Domains in Riemannian Manifolds with Nonvanishing Boundary Conditions -- On the Regularity of Nonlinear Subelliptic Equations -- Rigorous and Heuristic Treatment of Sensitive Singular Perturbations Arising in Elliptic Shells -- On the Existence of Positive Solutions of Semilinear Elliptic Inequalities on Riemannian Manifolds -- Recurrence Relations for Orthogonal Polynomials and Algebraicity of Solutions of the Dirichlet Problem -- On First Neumann Eigenvalue Bounds for Conformal Metrics -- Necessary Condition for the Regularity of a Boundary Point for Porous Medium Equations with Coefficients of Kato Class -- The Problem of Steady Flow over a Two-Dimensional Bottom Obstacle -- Well Posedness and Asymptotic Expansion of Solution of Stokes Equation Set in a Thin Cylindrical Elastic Tube -- On Solvability of Integral Equations for Harmonic Single Layer Potential on the Boundary of a Domain with Cusp -- H#x00F6;lder Estimates for Green#x2019;s Matrix of the Stokes System in Convex Polyhedra -- Boundary Integral Methods for Periodic Scattering Problems -- Boundary Coerciveness and the Neumann Problem for 4th Order Linear Partial Differential Operators En línea: http://dx.doi.org/10.1007/978-1-4419-1343-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33592 Ejemplares
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Título : Partial Differential Equations Tipo de documento: documento electrónico Autores: Jürgen Jost ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 214 Número de páginas: XIV, 410 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-4809-9 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Physics Differential Equations Theoretical, Mathematical and Computational Clasificación: 51 Matemáticas Resumen: This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research in elliptic partial differential equations. This revised and expanded third edition is enhanced with many additional examples that will help motivate the reader. New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including first-order hyperbolic systems, Langevin and Fokker-Planck equations, viscosity solutions for elliptic PDEs, and much more. Also, the new edition contains additional material on systems of elliptic partial differential equations, and it explains in more detail how the Harnack inequality can be used for the regularity of solutions Nota de contenido: Preface -- Introduction: What are Partial Differential Equations? -- 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order -- 2 The Maximum Principle -- 3 Existence Techniques I: Methods Based on the Maximum Principle -- 4 Existence Techniques II: Parabolic Methods. The Heat Equation -- 5 Reaction-Diffusion Equations and Systems -- 6 Hyperbolic Equations -- 7 The Heat Equation, Semigroups, and Brownian Motion.- 8 Relationships between Different Partial Differential Equations -- 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III) -- 10 Sobolev Spaces and L^2 Regularity theory -- 11 Strong solutions -- 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) -- 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash -- Appendix: Banach and Hilbert spaces. The L^p-Spaces -- References -- Index of Notation -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-4809-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32229 Partial Differential Equations [documento electrónico] / Jürgen Jost ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XIV, 410 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 214) .
ISBN : 978-1-4614-4809-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Physics Differential Equations Theoretical, Mathematical and Computational Clasificación: 51 Matemáticas Resumen: This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research in elliptic partial differential equations. This revised and expanded third edition is enhanced with many additional examples that will help motivate the reader. New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including first-order hyperbolic systems, Langevin and Fokker-Planck equations, viscosity solutions for elliptic PDEs, and much more. Also, the new edition contains additional material on systems of elliptic partial differential equations, and it explains in more detail how the Harnack inequality can be used for the regularity of solutions Nota de contenido: Preface -- Introduction: What are Partial Differential Equations? -- 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order -- 2 The Maximum Principle -- 3 Existence Techniques I: Methods Based on the Maximum Principle -- 4 Existence Techniques II: Parabolic Methods. The Heat Equation -- 5 Reaction-Diffusion Equations and Systems -- 6 Hyperbolic Equations -- 7 The Heat Equation, Semigroups, and Brownian Motion.- 8 Relationships between Different Partial Differential Equations -- 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III) -- 10 Sobolev Spaces and L^2 Regularity theory -- 11 Strong solutions -- 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) -- 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash -- Appendix: Banach and Hilbert spaces. The L^p-Spaces -- References -- Index of Notation -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-4809-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32229 Ejemplares
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Título : Partial Differential Equations Tipo de documento: documento electrónico Autores: Jürgen Jost ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 214 Número de páginas: XIV, 356 p. 10 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-49319-0 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Partial differential equations Physics Theoretical, and Computational Differential Equations Numerical Clasificación: 51 Matemáticas Resumen: This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods, and continuity methods. This book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. Connections between elliptic, parabolic, and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a one-year course on partial differential equations. For the new edition the author has added a new chapter on reaction-diffusion equations and systems. There is also new material on Neumann boundary value problems, Poincaré inequalities, expansions, as well as a new proof of the Hölder regularity of solutions of the Poisson equation. Jürgen Jost is Co-Director of the Max Planck Institute for Mathematics in the Sciences and Professor of Mathematics at the University of Leipzig. He is the author of a number of Springer books, including Dynamical Systems (2005), Postmodern Analysis (3rd ed. 2005, also translated into Japanese), Compact Riemann Surfaces (3rd ed. 2006) and Riemannian Geometry and Geometric Analysis (4th ed., 2005). The present book is an expanded translation of the original German version, Partielle Differentialgleichungen (1998). About the first edition: Because of the nice global presentation, I recommend this book to students and young researchers who need the now classical properties of these second-order partial differential equations. Teachers will also find in this textbook the basis of an introductory course on second-order partial differential equations. - Alain Brillard, Mathematical Reviews Beautifully written and superbly well-organised, I strongly recommend this book to anyone seeking a stylish, balanced, up-to-date survey of this central area of mathematics. - Nick Lord, The Mathematical Gazette Nota de contenido: Introduction: What Are Partial Differential Equations? -- The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order -- The Maximum Principle -- Existence Techniques I: Methods Based on the Maximum Principle -- Existence Techniques II: Parabolic Methods. The Heat Equation -- Reaction-Diffusion Equations and Systems -- The Wave Equation and its Connections with the Laplace and Heat Equations -- The Heat Equation, Semigroups, and Brownian Motion -- The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III) -- Sobolev Spaces and L2 Regularity Theory -- Strong Solutions -- The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) -- The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash En línea: http://dx.doi.org/10.1007/978-0-387-49319-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34490 Partial Differential Equations [documento electrónico] / Jürgen Jost ; SpringerLink (Online service) . - New York, NY : Springer New York, 2007 . - XIV, 356 p. 10 illus : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 214) .
ISBN : 978-0-387-49319-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Partial differential equations Physics Theoretical, and Computational Differential Equations Numerical Clasificación: 51 Matemáticas Resumen: This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods, and continuity methods. This book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. Connections between elliptic, parabolic, and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a one-year course on partial differential equations. For the new edition the author has added a new chapter on reaction-diffusion equations and systems. There is also new material on Neumann boundary value problems, Poincaré inequalities, expansions, as well as a new proof of the Hölder regularity of solutions of the Poisson equation. Jürgen Jost is Co-Director of the Max Planck Institute for Mathematics in the Sciences and Professor of Mathematics at the University of Leipzig. He is the author of a number of Springer books, including Dynamical Systems (2005), Postmodern Analysis (3rd ed. 2005, also translated into Japanese), Compact Riemann Surfaces (3rd ed. 2006) and Riemannian Geometry and Geometric Analysis (4th ed., 2005). The present book is an expanded translation of the original German version, Partielle Differentialgleichungen (1998). About the first edition: Because of the nice global presentation, I recommend this book to students and young researchers who need the now classical properties of these second-order partial differential equations. Teachers will also find in this textbook the basis of an introductory course on second-order partial differential equations. - Alain Brillard, Mathematical Reviews Beautifully written and superbly well-organised, I strongly recommend this book to anyone seeking a stylish, balanced, up-to-date survey of this central area of mathematics. - Nick Lord, The Mathematical Gazette Nota de contenido: Introduction: What Are Partial Differential Equations? -- The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order -- The Maximum Principle -- Existence Techniques I: Methods Based on the Maximum Principle -- Existence Techniques II: Parabolic Methods. The Heat Equation -- Reaction-Diffusion Equations and Systems -- The Wave Equation and its Connections with the Laplace and Heat Equations -- The Heat Equation, Semigroups, and Brownian Motion -- The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III) -- Sobolev Spaces and L2 Regularity Theory -- Strong Solutions -- The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) -- The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash En línea: http://dx.doi.org/10.1007/978-0-387-49319-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34490 Ejemplares
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Título : Partial Differential Equations 1 : Foundations and Integral Representations Tipo de documento: documento electrónico Autores: Sauvigny, Friedrich ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2012 Colección: Universitext, ISSN 0172-5939 Número de páginas: XV, 447 p. 16 illus Il.: online resource ISBN/ISSN/DL: 978-1-4471-2981-3 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Physics Differential Equations Mathematical Methods in Clasificación: 51 Matemáticas Resumen: This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this first volume, special emphasis is placed on geometric and complex variable methods involving integral representations. The following topics are treated: • integration and differentiation on manifolds • foundations of functional analysis • Brouwer's mapping degree • generalized analytic functions • potential theory and spherical harmonics • linear partial differential equations This new second edition of this volume has been thoroughly revised and a new section on the boundary behavior of Cauchy’s integral has been added. The second volume will present functional analytic methods and applications to problems in differential geometry. This textbook will be of particular use to graduate and postgraduate students interested in this field and will be of interest to advanced undergraduate students. It may also be used for independent study Nota de contenido: Differentiation and Integration on Manifolds -- Foundations of Functional Analysis -- Brouwer’s Degree of Mapping -- Generalized Analytic Functions -- Potential Theory and Spherical Harmonics -- Linear Partial Differential Equations in Rn En línea: http://dx.doi.org/10.1007/978-1-4471-2981-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32724 Partial Differential Equations 1 : Foundations and Integral Representations [documento electrónico] / Sauvigny, Friedrich ; SpringerLink (Online service) . - London : Springer London, 2012 . - XV, 447 p. 16 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4471-2981-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Physics Differential Equations Mathematical Methods in Clasificación: 51 Matemáticas Resumen: This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this first volume, special emphasis is placed on geometric and complex variable methods involving integral representations. The following topics are treated: • integration and differentiation on manifolds • foundations of functional analysis • Brouwer's mapping degree • generalized analytic functions • potential theory and spherical harmonics • linear partial differential equations This new second edition of this volume has been thoroughly revised and a new section on the boundary behavior of Cauchy’s integral has been added. The second volume will present functional analytic methods and applications to problems in differential geometry. This textbook will be of particular use to graduate and postgraduate students interested in this field and will be of interest to advanced undergraduate students. It may also be used for independent study Nota de contenido: Differentiation and Integration on Manifolds -- Foundations of Functional Analysis -- Brouwer’s Degree of Mapping -- Generalized Analytic Functions -- Potential Theory and Spherical Harmonics -- Linear Partial Differential Equations in Rn En línea: http://dx.doi.org/10.1007/978-1-4471-2981-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32724 Ejemplares
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