Overview

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.

Full Product Details

Author:   Stefano Bianchini ,  Eric A. Carlen ,  Alexander Mielke ,  Cédric Villani
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Volume:   2028
Dimensions:   Width: 15.50cm , Height: 1.00cm , Length: 23.50cm
Weight:   0.373kg
ISBN:  

9783642217180

ISBN 10:   3642217184
Pages:   224
Publication Date:   30 July 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

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.

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