Authors:
- Complements Adams’ Sobolev Spaces in comprising a complete presentation of functional spaces but combined with abstract convex analysis
- Gathers together results from functional analysis that make it easier to understand the nature and properties of the functions occurring in these equations, as well as the constraints they must obey to qualify as solutions
- Provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
About this book
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.
Authors and Affiliations
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Département de Mathématiques, Université de Cergy-Pontoise, Cergy-Pontoise Cedex, France
Françoise Demengel
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Paris Cedex 13, France
Gilbert Demengel
Bibliographic Information
Book Title: Functional Spaces for the Theory of Elliptic Partial Differential Equations
Authors: Françoise Demengel, Gilbert Demengel
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4471-2807-6
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London Limited 2012
Softcover ISBN: 978-1-4471-2806-9Published: 23 January 2012
eBook ISBN: 978-1-4471-2807-6Published: 24 January 2012
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XVIII, 465
Number of Illustrations: 11 b/w illustrations