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＜電子ブック＞
Nonlinear PDE’s and Applications : C.I.M.E. Summer School, Cetraro, Italy 2008, Editors: Luigi Ambrosio, Giuseppe Savaré / by Stefano Bianchini, Eric A. Carlen, Alexander Mielke, Cédric Villani
(C.I.M.E. Foundation Subseries. ISSN:29461820 ; 2028)

版	1st ed. 2011.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2011
本文言語	英語
大きさ	XIII, 224 p. 8 illus., 7 illus. in color : online resource
著者標目	*Bianchini, Stefano author Carlen, Eric A author Mielke, Alexander author Villani, Cédric author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Differential equations LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Functional analysis LCSH:Geometry, Differential FREE:Analysis FREE:Differential Equations FREE:Calculus of Variations and Optimization FREE:Functional Analysis FREE:Differential Geometry
一般注記	Transport Rays and Applications to Hamilton-Jacobi Equations -- Functional Inequalities and Dynamics -- Differential, Energetic, and Metric Formulations for Rate-independent Processes -- Optimal Transport and Curvature This volume collects the notes of the CIME course "Nonlinear PDE’s and applications" held in Cetraro (Italy) on June 23–28, 2008. It consists of four series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), and Cédric Villani (Ecole Normale Superieure de Lyon). They presented a broad overview of far-reaching findings and exciting new developments concerning, in particular, optimal transport theory, nonlinear evolution equations, functional inequalities, and differential geometry. A sampling of the main topics considered here includes optimal transport, Hamilton-Jacobi equations, Riemannian geometry, and their links with sharp geometric/functional inequalities, variational methods for studying nonlinear evolution equations and their scaling properties, and the metric/energetic theory of gradient flows and of rate-independent evolution problems. The book explores the fundamental connections between all of these topics and points to new research directions in contributions by leading experts in these fields HTTP:URL=https://doi.org/10.1007/978-3-642-21861-3

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