Authors:
- 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 book series: Universitext (UTX)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
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.
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
- partial differential equations
Authors and Affiliations
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Laboratoire Jacques-Louis Lions, Sorbonne Université, Paris, France
Hervé Le Dret
About the author
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
Book Title: Nonlinear Elliptic Partial Differential Equations
Book Subtitle: An Introduction
Authors: Hervé Le Dret
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-78390-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-78389-5Published: 05 June 2018
eBook ISBN: 978-3-319-78390-1Published: 25 May 2018
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
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
Topics: Partial Differential Equations, Calculus of Variations and Optimal Control; Optimization, Functional Analysis