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Nonlinear Elliptic Partial Differential Equations

An Introduction


  • 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


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


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.


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

  1. 1.Laboratoire Jacques-Louis LionsSorbonne UniversitéParisFrance

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.

Bibliographic information

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