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9783642217180

Nonlinear PDE⿿s and Applications : C. I. M. E. Summer School, Cetraro, Italy 2008, Editors: Luigi Ambrosio, Giuseppe Savaré

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  • ISBN13:

    9783642217180

  • ISBN10:

    3642217184

  • Format: Paperback
  • Copyright: 2011-08-09
  • Publisher: Springer Verlag
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Summary

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.

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