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

Part of the Lecture Notes in Mathematics book series (LNM, volume 2028)

Also part of the C.I.M.E. Foundation Subseries book sub series (LNMCIME, volume 2028)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Stefano Bianchini, Matteo Gloyer
    Pages 1-15
  3. Eric A. Carlen
    Pages 17-85
  4. Alessio Figalli, Cédric Villani
    Pages 171-217
  5. Back Matter
    Pages 219-224

About this book


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.


35-XX, 49-XX, 46-XX, 53-XX Functional inequalities Nonlinear evolution equations Optimal transport Rate independent processes

Authors and affiliations

  • Stefano Bianchini
    • 1
  • Eric A. Carlen
    • 2
  • Alexander Mielke
    • 3
  • Cédric Villani
    • 4
  1. 1.SISSA-ISASTriesteItaly
  2. 2.Department of Mathematics, Hill CenterRutgers UniversityPiscatawayUSA
  3. 3.Analysis und Stochastik (WIAS)Weierstraß-Institut für AngewandteBerlinGermany
  4. 4.Institut Henri PoincaréParis, Cedex 05USA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-21718-0
  • Online ISBN 978-3-642-21861-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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