Functional Spaces for the Theory of Elliptic Partial Differential Equations (Universitext)
Language: English
Published by Springer, 2012
Series: Book 95 of 261 - Universitext
- Softcover
- Used
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- Title
- Functional Spaces for the Theory of Elliptic Partial Differential Equations (Universitext)
- Author
- Demengel, Françoise, Demengel, Gilbert
- Publisher
- Springer
- Publication year
- 2012
- Condition
- Like New
- Book Type
- book
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1447128060
- ISBN 13
- 9781447128069
- Series
- Book 95 of 261: Universitext
The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions.
This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem.
The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space.
There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.
"Synopsis" may belong to another edition of this title.
From the Back Cover
Linear and non-linear elliptic boundary problems are a fundamental subject in analysis and the spaces of weakly differentiable functions (also called Sobolev spaces) are an essential tool for analysing the regularity of its solutions.
The complete theory of Sobolev spaces is covered whilst also explaining how abstract convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. Other kinds of functional spaces are also included, useful for treating variational problems such as the minimal surface problem.
Almost every result comes with a complete and detailed proof. In some cases, more than one proof is provided in order to highlight different aspects of the result. A range of exercises of varying levels of difficulty concludes each chapter with hints to solutions for many of them.
It is hoped that this book will provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on Schwartz spaces.
"About the title" may belong to another edition of this title.
Mispah books
Redhill, Surrey, United Kingdom
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