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＜電子ブック＞
Nonlinear Elliptic Partial Differential Equations : An Introduction / by Hervé Le Dret
(Universitext. ISSN:21916675)

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2018
大きさ	X, 253 p. 71 illus., 23 illus. in color : online resource
著者標目	*Le Dret, Hervé author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Functional analysis FREE:Differential Equations FREE:Calculus of Variations and Optimization FREE:Functional Analysis
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-78390-1

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