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Universitext

Nonlinear Elliptic Partial Differential Equations

An Introduction

Authors: Le Dret, Herve

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  • Introduces several mathematical techniques relevant to solving boundary value problems involving nonlinear elliptic PDEs
  • Provides the essentials of test-function and distribution spaces
  • Includes 44 exercises and problems
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  • ISBN 978-3-319-78390-1
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About this Textbook

This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations.

After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations.

Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.


About the authors

Hervé Le Dret is Professor of Mathematics at the Laboratoire Jacques-Louis Lions, Sorbonne Université, Paris, France. He recently completed two consecutive five-year terms as Dean of the Faculty of Mathematics and is now back to regular teaching and research duties. His research focuses on partial differential equations in mechanics, calculus of variations and numerical analysis.

Table of contents (8 chapters)

Table of contents (8 chapters)
  • A Brief Review of Real and Functional Analysis

    Pages 1-46

    Le Dret, Hervé

  • Fixed Point Theorems and Applications

    Pages 47-68

    Le Dret, Hervé

  • Superposition Operators

    Pages 69-91

    Le Dret, Hervé

  • The Galerkin Method

    Pages 93-109

    Le Dret, Hervé

  • The Maximum Principle, Elliptic Regularity, and Applications

    Pages 111-140

    Le Dret, Hervé

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-319-78390-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Elliptic Partial Differential Equations
Book Subtitle
An Introduction
Authors
Series Title
Universitext
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-78390-1
DOI
10.1007/978-3-319-78390-1
Softcover ISBN
978-3-319-78389-5
Series ISSN
0172-5939
Edition Number
1
Number of Pages
X, 253
Number of Illustrations
48 b/w illustrations, 23 illustrations in colour
Additional Information
Original French edition published by Springer-Verlag Berlin Heidelberg, 2013
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