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Nonlinear PDE’s and Applications

C.I.M.E. Summer School, Cetraro, Italy 2008, Editors: Luigi Ambrosio, Giuseppe Savaré

Stefano Bianchini, Eric A. Carlen, Alexander Mielke, Cédric Villani (Autoren)

Buch | Softcover

XIII, 224 Seiten

2011 | 2011
Springer Berlin (Verlag)
978-3-642-21718-0 (ISBN)

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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.

Cédric Villani, geboren 1973, gehört zu den weltweit führenden und innovativsten Mathematikern. Für seine Forschung erhielt er mehrere Preise, u.a. 2010 die renommierte Fields-Medaille, das Äquivalent zum Nobelpreis. Villani ist Professor für Mathematik an der École Normale Supérieure in Lyon und Direktor des Institut Henri Poincaré in Paris.

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.

Erscheint lt. Verlag	30.7.2011
Reihe/Serie	C.I.M.E. Foundation Subseries
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XIII, 224 p. 8 illus., 7 illus. in color.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	366 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	35-XX, 49-XX, 46-XX, 53-XX • Analysis • functional inequalities • nonlinear evolution equations • optimal transport • Partial differential equations • Rate independent processes
ISBN-10	3-642-21718-4 / 3642217184
ISBN-13	978-3-642-21718-0 / 9783642217180
Zustand	Neuware