Nonlinear Elliptic Partial Differential Equations
An Introduction
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Beschreibung
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.
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
Autor*in
Hervé Le Dret
Themen in »Nonlinear Elliptic Partial Differential Equations«
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