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## Autor Mariano Giaquinta |

### Documentos disponibles escritos por este autor (4)

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An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs / Mariano Giaquinta (2012)

Título : An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs Tipo de documento: documento electrónico Autores: Mariano Giaquinta ; SpringerLink (Online service) ; Luca Martinazzi Editorial: Pisa : Scuola Normale Superiore Fecha de publicación: 2012 Colección: Publications of the Scuola Normale Superiore Número de páginas: XIII, 370 p Il.: online resource ISBN/ISSN/DL: 978-88-7642-443-4 Idioma : Inglés ( eng)Palabras clave: Mathematics Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certain assumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to as regularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of the basic ideas and techniques introduced in this context, confining ourselves to important but simple situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, direct methods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and Lp-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar case and partial regularity theorems in the vector valued case; energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensional weakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of the Lp theory, including the celebrated results of Wente and of Coifman-Lions-Meyer-Semmes Nota de contenido: 1 Harmonic functions -- 2 Direct methods -- 3 Hilbert space methods -- 4 L2-regularity: the Caccioppoli inequality -- 5 Schauder estimates -- 6 Some real analysis -- 7 Lp-theory -- 8 The regularity problem in the scalar case -- 9 Partial regularity in the vector-valued case -- 10 Harmonic maps -- 11 A survey of minimal graphs En línea: http://dx.doi.org/10.1007/978-88-7642-443-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33055 An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs [documento electrónico] / Mariano Giaquinta ; SpringerLink (Online service) ; Luca Martinazzi . - Pisa : Scuola Normale Superiore, 2012 . - XIII, 370 p : online resource. - (Publications of the Scuola Normale Superiore) .ISBN: 978-88-7642-443-4

Idioma : Inglés (eng)

Palabras clave: Mathematics Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certain assumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to as regularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of the basic ideas and techniques introduced in this context, confining ourselves to important but simple situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, direct methods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and Lp-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar case and partial regularity theorems in the vector valued case; energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensional weakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of the Lp theory, including the celebrated results of Wente and of Coifman-Lions-Meyer-Semmes Nota de contenido: 1 Harmonic functions -- 2 Direct methods -- 3 Hilbert space methods -- 4 L2-regularity: the Caccioppoli inequality -- 5 Schauder estimates -- 6 Some real analysis -- 7 Lp-theory -- 8 The regularity problem in the scalar case -- 9 Partial regularity in the vector-valued case -- 10 Harmonic maps -- 11 A survey of minimal graphs En línea: http://dx.doi.org/10.1007/978-88-7642-443-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33055 ## Ejemplares

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Título : Mathematical Analysis : An Introduction to Functions of Several Variables Tipo de documento: documento electrónico Autores: Mariano Giaquinta ; SpringerLink (Online service) ; Giuseppe Modica Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2009 Número de páginas: XII, 348 p. 105 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4612-7 Idioma : Inglés ( eng)Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Measure theory Differential equations Functions of complex variables Calculus variations and Integration Variations Optimal Control; Optimization Several Complex Variables Analytic Spaces Ordinary Equations Clasificación: 51 Matemáticas Resumen: This text introduces basic ideas, structures, and results of differential and integral calculus for functions of several variables. The presentation is engaging and motivates the reader with numerous examples, remarks, illustrations, and exercises. Mathematical Analysis: An Introduction to Functions of Several Variables may be used in the classroom setting for advanced undergraduate and graduate students or as a self-study. It is also a valuable reference for researchers in most mathematical disciplines. An appendix highlights mathematicians and scientists who have made important contributions in the development of theories in the subject. Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis. Reviews of previous volumes in Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. . . . This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties. —Journal of Analysis and its Applications The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations. —Zentralblatt MATH Nota de contenido: Differential Calculus -- Integral Calculus -- Curves and Differential Forms -- Holomorphic Functions -- Surfaces and Level Sets -- Systems of Ordinary Differential Equations En línea: http://dx.doi.org/10.1007/978-0-8176-4612-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33934 Mathematical Analysis : An Introduction to Functions of Several Variables [documento electrónico] / Mariano Giaquinta ; SpringerLink (Online service) ; Giuseppe Modica . - Boston, MA : Birkhäuser Boston, 2009 . - XII, 348 p. 105 illus : online resource.ISBN: 978-0-8176-4612-7

Idioma : Inglés (eng)

Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Measure theory Differential equations Functions of complex variables Calculus variations and Integration Variations Optimal Control; Optimization Several Complex Variables Analytic Spaces Ordinary Equations Clasificación: 51 Matemáticas Resumen: This text introduces basic ideas, structures, and results of differential and integral calculus for functions of several variables. The presentation is engaging and motivates the reader with numerous examples, remarks, illustrations, and exercises. Mathematical Analysis: An Introduction to Functions of Several Variables may be used in the classroom setting for advanced undergraduate and graduate students or as a self-study. It is also a valuable reference for researchers in most mathematical disciplines. An appendix highlights mathematicians and scientists who have made important contributions in the development of theories in the subject. Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis. Reviews of previous volumes in Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. . . . This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties. —Journal of Analysis and its Applications The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations. —Zentralblatt MATH Nota de contenido: Differential Calculus -- Integral Calculus -- Curves and Differential Forms -- Holomorphic Functions -- Surfaces and Level Sets -- Systems of Ordinary Differential Equations En línea: http://dx.doi.org/10.1007/978-0-8176-4612-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33934 ## Ejemplares

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Título : Mathematical Analysis : Foundations and Advanced Techniques for Functions of Several Variables Tipo de documento: documento electrónico Autores: Mariano Giaquinta ; SpringerLink (Online service) ; Giuseppe Modica Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2012 Número de páginas: XIII, 405 p. 66 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-8310-8 Idioma : Inglés ( eng)Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Clasificación: 51 Matemáticas Resumen: Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory. The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differential forms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics. The authors conclude with the study of measure and integration theory – Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This work may be used as a supplementary text in the classroom or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengths of this presentation, along with the other four books on analysis published by the authors, is the motivation for understanding the subject through examples, observations, exercises, and illustrations. Other books published by the authors – all of which provide the reader with a strong foundation in modern-day analysis – include: * Mathematical Analysis: Functions of One Variable * Mathematical Analysis: Approximation and Discrete Processes * Mathematical Analysis: Linear and Metric Structures and Continuity * Mathematical Analysis: An Introduction to Functions of Several Variables Reviews of previous volumes of Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. . . . This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties. —Journal of Analysis and its Applications The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature of this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations. —Zentralblatt MATH Nota de contenido: Preface -- Spaces of Summable Functions and Partial Differential Equations -- Convex Sets and Convex Functions -- The Formalism of the Calculus of Variations -- Differential Forms -- Measures and Integrations -- Hausdorff and Radon Measures -- Mathematicians and Other Scientists -- Bibliographical Notes -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8310-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32692 Mathematical Analysis : Foundations and Advanced Techniques for Functions of Several Variables [documento electrónico] / Mariano Giaquinta ; SpringerLink (Online service) ; Giuseppe Modica . - Boston : Birkhäuser Boston, 2012 . - XIII, 405 p. 66 illus : online resource.ISBN: 978-0-8176-8310-8

Idioma : Inglés (eng)

Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Clasificación: 51 Matemáticas Resumen: Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory. The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differential forms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics. The authors conclude with the study of measure and integration theory – Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This work may be used as a supplementary text in the classroom or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengths of this presentation, along with the other four books on analysis published by the authors, is the motivation for understanding the subject through examples, observations, exercises, and illustrations. Other books published by the authors – all of which provide the reader with a strong foundation in modern-day analysis – include: * Mathematical Analysis: Functions of One Variable * Mathematical Analysis: Approximation and Discrete Processes * Mathematical Analysis: Linear and Metric Structures and Continuity * Mathematical Analysis: An Introduction to Functions of Several Variables Reviews of previous volumes of Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. . . . This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties. —Journal of Analysis and its Applications The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature of this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations. —Zentralblatt MATH Nota de contenido: Preface -- Spaces of Summable Functions and Partial Differential Equations -- Convex Sets and Convex Functions -- The Formalism of the Calculus of Variations -- Differential Forms -- Measures and Integrations -- Hausdorff and Radon Measures -- Mathematicians and Other Scientists -- Bibliographical Notes -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8310-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32692 ## Ejemplares

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Título : Mathematical Analysis : Linear and Metric Structures and Continuity Tipo de documento: documento electrónico Autores: Mariano Giaquinta ; SpringerLink (Online service) ; Giuseppe Modica Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2007 Número de páginas: XX, 466 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4514-4 Idioma : Inglés ( eng)Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Differential equations Functions of real variables Applied mathematics Engineering Topology Ordinary Equations Real Applications Clasificación: 51 Matemáticas Resumen: This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces. The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators. Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis Nota de contenido: Linear Algebra -- Vectors, Matrices and Linear Systems -- Vector Spaces and Linear Maps -- Euclidean and Hermitian Spaces -- Self-Adjoint Operators -- Metrics and Topology -- Metric Spaces and Continuous Functions -- Compactness and Connectedness -- Curves -- Some Topics from the Topology of ?n -- Continuity in Infinite-Dimensional Spaces -- Spaces of Continuous Functions, Banach Spaces and Abstract Equations -- Hilbert Spaces, Dirichlet’s Principle and Linear Compact Operators -- Some Applications En línea: http://dx.doi.org/10.1007/978-0-8176-4514-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34541 Mathematical Analysis : Linear and Metric Structures and Continuity [documento electrónico] / Mariano Giaquinta ; SpringerLink (Online service) ; Giuseppe Modica . - Boston, MA : Birkhäuser Boston, 2007 . - XX, 466 p : online resource.ISBN: 978-0-8176-4514-4

Idioma : Inglés (eng)

Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Differential equations Functions of real variables Applied mathematics Engineering Topology Ordinary Equations Real Applications Clasificación: 51 Matemáticas Resumen: This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces. The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators. Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis Nota de contenido: Linear Algebra -- Vectors, Matrices and Linear Systems -- Vector Spaces and Linear Maps -- Euclidean and Hermitian Spaces -- Self-Adjoint Operators -- Metrics and Topology -- Metric Spaces and Continuous Functions -- Compactness and Connectedness -- Curves -- Some Topics from the Topology of ?n -- Continuity in Infinite-Dimensional Spaces -- Spaces of Continuous Functions, Banach Spaces and Abstract Equations -- Hilbert Spaces, Dirichlet’s Principle and Linear Compact Operators -- Some Applications En línea: http://dx.doi.org/10.1007/978-0-8176-4514-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34541 ## Ejemplares

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