Nonlinear Elliptic Partial Differential Equations An 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.

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.