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Nonlinear Elliptic Partial Differential Equations

An Introduction

  • Hervé Le Dret

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-x
  2. Hervé Le Dret
    Pages 47-68
  3. Hervé Le Dret
    Pages 69-91
  4. Hervé Le Dret
    Pages 93-109
  5. Hervé Le Dret
    Pages 179-213
  6. Back Matter
    Pages 245-253

About this book

Introduction

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.

Keywords

nonlinear elliptic partial differential equations fixed point theorems fixed point theorems applications superposition operators Young measures Galerkin method maximum principle elliptic regularity super-solutions and sub-solutions direct method calculus of variations Euler-Lagrange equation quasiconvexity polyconvexity rank-1 convexity mountain pass lemma monotone operators variational inequalities calculus of variations and critical points calculus of variations and quasilinear problems

Authors and affiliations

  • Hervé Le Dret
    • 1
  1. 1.Laboratoire Jacques-Louis LionsSorbonne UniversitéParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-78390-1
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-78389-5
  • Online ISBN 978-3-319-78390-1
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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