Universitext

Functional Spaces for the Theory of Elliptic Partial Differential Equations

Authors: Demengel, Françoise, Demengel, Gilbert

  • 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
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eBook $59.99
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  • ISBN 978-1-4471-2807-6
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price for USA
  • ISBN 978-1-4471-2806-9
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About this Textbook

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.

Table of contents (8 chapters)

  • Notions from Topology and Functional Analysis

    Demengel, Françoise (et al.)

    Pages 1-55

  • Sobolev Spaces and Embedding Theorems

    Demengel, Françoise (et al.)

    Pages 57-112

  • Traces of Functions on Sobolev Spaces

    Demengel, Françoise (et al.)

    Pages 113-177

  • Fractional Sobolev Spaces

    Demengel, Françoise (et al.)

    Pages 179-228

  • Elliptic PDE: Variational Techniques

    Demengel, Françoise (et al.)

    Pages 229-298

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4471-2807-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.95
price for USA
  • ISBN 978-1-4471-2806-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Functional Spaces for the Theory of Elliptic Partial Differential Equations
Authors
Translated by
Erné, R.
Series Title
Universitext
Copyright
2012
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
Distribution Rights
Exclusive distribution rights in France: EDP Sciences, France
eBook ISBN
978-1-4471-2807-6
DOI
10.1007/978-1-4471-2807-6
Softcover ISBN
978-1-4471-2806-9
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XVIII, 465
Number of Illustrations and Tables
11 b/w illustrations
Topics