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Mathematics - Dynamical Systems & Differential Equations | Functional Spaces for the Theory of Elliptic Partial Differential Equations

Functional Spaces for the Theory of Elliptic Partial Differential Equations

Series: Universitext

Demengel, Françoise, Demengel, Gilbert

Translated by Erné, R.

2012, XVIII, 465 p. 11 illus.

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  • 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

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.

Content Level » Graduate

Keywords » Sobolev spaces - distributions - elliptic partial differential equations - function spaces

Related subjects » Analysis - Dynamical Systems & Differential Equations

Table of contents / Preface / Sample pages 

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Exclusive distribution rights in France: EDP Sciences, France

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