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

Autorentext

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.

Zusammenfassung

Inhalt
1 A brief review of real and functional analysis.- 2 Fixed point theorems and applications.- 3 Superposition operators.- 4 The Galerkin method.- 5 The maximum principle, elliptic regularity, and applications.- 6 Calculus of variations and quasilinear problems.- 7 Calculus of variations and critical points.- 8 Monotone operators and variational inequalities.- References.- Index.