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Título : Elliptic Partial Differential Equations : Volume 1: Fredholm Theory of Elliptic Problems in Unbounded Domains Tipo de documento: documento electrónico Autores: Volpert, Vitaly ; SpringerLink (Online service) Editorial: Basel : Springer Basel Fecha de publicación: 2011 Colección: Monographs in Mathematics, ISSN 1017-0480 num. 101 Número de páginas: XVIII, 642 p Il.: online resource ISBN/ISSN/DL: 978-3-0346-0537-3 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments.
The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.
Nota de contenido: Chapter 1. Introduction -- Chapter 2. Function spaces and operators -- Chapter 3. A priori estimates -- Chapter 4. Normal solvability -- Chapter 5. Fredholm property -- Chapter 6. Formally adjoint problems -- Chapter 7. Elliptic problems with a parameter -- Chapter 8. Index of elliptic operators -- Chapter 9. Problems in cylinders -- Chapter 10. Non-Fredholm operators -- Chapter 11. Nonlinear Fredholm operators -- Supplement. Discrete operators.-Historical and bibliographical comments -- Acknowledgements -- References En línea: http://dx.doi.org/10.1007/978-3-0346-0537-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33244 Elliptic Partial Differential Equations : Volume 1: Fredholm Theory of Elliptic Problems in Unbounded Domains [documento electrónico] / Volpert, Vitaly ; SpringerLink (Online service) . - Basel : Springer Basel, 2011 . - XVIII, 642 p : online resource. - (Monographs in Mathematics, ISSN 1017-0480; 101) .
ISBN : 978-3-0346-0537-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments.
The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.
Nota de contenido: Chapter 1. Introduction -- Chapter 2. Function spaces and operators -- Chapter 3. A priori estimates -- Chapter 4. Normal solvability -- Chapter 5. Fredholm property -- Chapter 6. Formally adjoint problems -- Chapter 7. Elliptic problems with a parameter -- Chapter 8. Index of elliptic operators -- Chapter 9. Problems in cylinders -- Chapter 10. Non-Fredholm operators -- Chapter 11. Nonlinear Fredholm operators -- Supplement. Discrete operators.-Historical and bibliographical comments -- Acknowledgements -- References En línea: http://dx.doi.org/10.1007/978-3-0346-0537-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33244 Ejemplares
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Título : Methods of Geometric Analysis in Extension and Trace Problems : Volume 1 Tipo de documento: documento electrónico Autores: Brudnyi, Alexander ; SpringerLink (Online service) ; Brudnyi, Yuri Editorial: Basel : Springer Basel Fecha de publicación: 2012 Colección: Monographs in Mathematics, ISSN 1017-0480 num. 102 Número de páginas: XXIV, 564 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0209-3 Idioma : Inglés (eng) Palabras clave: Mathematics Functional analysis Analysis Clasificación: 51 Matemáticas Resumen: This is the first of a two-volume work presenting a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers the development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific, these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the work is also unified by the geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and Coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience Nota de contenido: Preface -- Basic Terms and Notation -- Part 1. Classical Extension-Trace Theorems and Related Results -- Chapter 1. Continuous and Lipschitz Functions -- Chapter 2. Smooth Functions on Subsets of Rn -- Part 2. Topics in Geometry of and Analysis on Metric Spaces -- Chapter 3. Topics in Metric Space Theory -- Chapter 4. Selected Topics in Analysis on Metric Spaces -- Chapter 5. Lipschitz Embedding and Selections -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0209-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32862 Methods of Geometric Analysis in Extension and Trace Problems : Volume 1 [documento electrónico] / Brudnyi, Alexander ; SpringerLink (Online service) ; Brudnyi, Yuri . - Basel : Springer Basel, 2012 . - XXIV, 564 p : online resource. - (Monographs in Mathematics, ISSN 1017-0480; 102) .
ISBN : 978-3-0348-0209-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Functional analysis Analysis Clasificación: 51 Matemáticas Resumen: This is the first of a two-volume work presenting a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers the development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific, these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the work is also unified by the geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and Coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience Nota de contenido: Preface -- Basic Terms and Notation -- Part 1. Classical Extension-Trace Theorems and Related Results -- Chapter 1. Continuous and Lipschitz Functions -- Chapter 2. Smooth Functions on Subsets of Rn -- Part 2. Topics in Geometry of and Analysis on Metric Spaces -- Chapter 3. Topics in Metric Space Theory -- Chapter 4. Selected Topics in Analysis on Metric Spaces -- Chapter 5. Lipschitz Embedding and Selections -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0209-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32862 Ejemplares
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Título : Methods of Geometric Analysis in Extension and Trace Problems : Volume 2 Tipo de documento: documento electrónico Autores: Brudnyi, Alexander ; SpringerLink (Online service) ; Brudnyi, Yuri Editorial: Basel : Springer Basel Fecha de publicación: 2012 Colección: Monographs in Mathematics, ISSN 1017-0480 num. 103 Número de páginas: XX, 416 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0212-3 Idioma : Inglés (eng) Palabras clave: Mathematics Functional analysis Analysis Clasificación: 51 Matemáticas Resumen: This is the second of a two-volume work presenting a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers the development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific, these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the work is also unified by the geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and Coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience Nota de contenido: Part 3. Lipschitz Extensions from Subsets of Metric Spaces -- Chapter 6. Extensions of Lipschitz Maps -- Chapter 7. Simultaneous Lipschitz Extensions -- Chapter 8. Linearity and Nonlinearity -- Part 4. Smooth Extension and Trace Problems for Functions on Subsets of Rn -- Chapter 9. Traces to Closed Subsets: Criteria, Applications -- Chapter 10. Whitney Problems -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0212-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32863 Methods of Geometric Analysis in Extension and Trace Problems : Volume 2 [documento electrónico] / Brudnyi, Alexander ; SpringerLink (Online service) ; Brudnyi, Yuri . - Basel : Springer Basel, 2012 . - XX, 416 p : online resource. - (Monographs in Mathematics, ISSN 1017-0480; 103) .
ISBN : 978-3-0348-0212-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Functional analysis Analysis Clasificación: 51 Matemáticas Resumen: This is the second of a two-volume work presenting a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers the development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific, these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the work is also unified by the geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and Coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience Nota de contenido: Part 3. Lipschitz Extensions from Subsets of Metric Spaces -- Chapter 6. Extensions of Lipschitz Maps -- Chapter 7. Simultaneous Lipschitz Extensions -- Chapter 8. Linearity and Nonlinearity -- Part 4. Smooth Extension and Trace Problems for Functions on Subsets of Rn -- Chapter 9. Traces to Closed Subsets: Criteria, Applications -- Chapter 10. Whitney Problems -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0212-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32863 Ejemplares
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Título : Vector-valued Laplace Transforms and Cauchy Problems : Second Edition Tipo de documento: documento electrónico Autores: Wolfgang Arendt ; SpringerLink (Online service) ; Charles J.K. Batty ; Hieber, Matthias ; Neubrander, Frank Editorial: Basel : Springer Basel Fecha de publicación: 2011 Colección: Monographs in Mathematics, ISSN 1017-0480 num. 96 Número de páginas: XII, 540 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0087-7 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are studied. Diverse applications to partial differential equations are given. The book contains an introduction to the Bochner integral and several appendices on background material. It is addressed to students and researchers interested in evolution equations, Laplace and Fourier transforms, and functional analysis. The authors have succeeded admirably in bringing together a wealth of recent material, much of which appears in book form for the first time. This authoritative work is likely to become a standard reference on both the Laplace transform and its applications to the abstract Cauchy problem. … The book is an excellent textbook as well. Proofs are always transparent and complete, and many topics that could have been considered as background material are covered as well. All this makes the text very accessible and self-contained. Applications to concrete differential operators are given throughout the text. Each chapter ends with historical and bibliographical comments. … In summary, this book will be of interest to a wide audience of (functional) analysts and it should have a place in every mathematics library. Warmly recommended! Jan van Neerven, Nieuw Archief voor Wiskunde, No. 3, 2003 Nota de contenido: Preface to the First Edition -- Preface to the Second Edition -- I Laplace Transforms and Well-Posedness of Cauchy Problems -- 1 The Laplace Integral -- 2 The Laplace Transform -- 3 Cauchy Problems -- II Tauberian Theorems and Cauchy Problems -- 4 Asymptotics of Laplace Transforms -- 5 Asymptotics of Solutions of Cauchy Problems -- III Applications and Examples -- 6 The Heat Equation -- 7 The Wave Equation -- 8 Translation Invariant Operators on Lp(Rn) -- A Vector-valued Holomorphic Functions -- B Closed Operators -- C Ordered Banach Spaces -- D Banach Spaces which Contain c0 -- E Distributions and Fourier Multipliers -- Bibliography -- Notation -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0087-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33259 Vector-valued Laplace Transforms and Cauchy Problems : Second Edition [documento electrónico] / Wolfgang Arendt ; SpringerLink (Online service) ; Charles J.K. Batty ; Hieber, Matthias ; Neubrander, Frank . - Basel : Springer Basel, 2011 . - XII, 540 p : online resource. - (Monographs in Mathematics, ISSN 1017-0480; 96) .
ISBN : 978-3-0348-0087-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are studied. Diverse applications to partial differential equations are given. The book contains an introduction to the Bochner integral and several appendices on background material. It is addressed to students and researchers interested in evolution equations, Laplace and Fourier transforms, and functional analysis. The authors have succeeded admirably in bringing together a wealth of recent material, much of which appears in book form for the first time. This authoritative work is likely to become a standard reference on both the Laplace transform and its applications to the abstract Cauchy problem. … The book is an excellent textbook as well. Proofs are always transparent and complete, and many topics that could have been considered as background material are covered as well. All this makes the text very accessible and self-contained. Applications to concrete differential operators are given throughout the text. Each chapter ends with historical and bibliographical comments. … In summary, this book will be of interest to a wide audience of (functional) analysts and it should have a place in every mathematics library. Warmly recommended! Jan van Neerven, Nieuw Archief voor Wiskunde, No. 3, 2003 Nota de contenido: Preface to the First Edition -- Preface to the Second Edition -- I Laplace Transforms and Well-Posedness of Cauchy Problems -- 1 The Laplace Integral -- 2 The Laplace Transform -- 3 Cauchy Problems -- II Tauberian Theorems and Cauchy Problems -- 4 Asymptotics of Laplace Transforms -- 5 Asymptotics of Solutions of Cauchy Problems -- III Applications and Examples -- 6 The Heat Equation -- 7 The Wave Equation -- 8 Translation Invariant Operators on Lp(Rn) -- A Vector-valued Holomorphic Functions -- B Closed Operators -- C Ordered Banach Spaces -- D Banach Spaces which Contain c0 -- E Distributions and Fourier Multipliers -- Bibliography -- Notation -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0087-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33259 Ejemplares
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