C.I.M.E. Foundation Subseries

Nonlinear PDE’s and Applications

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

Authors: Bianchini, S., Carlen, E.A., Mielke, A., Villani, C.

  • A broad overview on some deep results and new exciting developments
  • Contribution of leading experts
  • Accessible introduction to new theories and results
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  • ISBN 978-3-642-21861-3
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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.

Table of contents (4 chapters)

  • Transport Rays and Applications to Hamilton–Jacobi Equations

    Bianchini, Stefano (et al.)

    Pages 1-15

  • Functional Inequalities and Dynamics

    Carlen, Eric A.

    Pages 17-85

  • Differential, Energetic, and Metric Formulations for Rate-Independent Processes

    Mielke, Alexander

    Pages 87-170

  • Optimal Transport and Curvature

    Figalli, Alessio (et al.)

    Pages 171-217

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-21861-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-642-21718-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear PDE’s and Applications
Book Subtitle
C.I.M.E. Summer School, Cetraro, Italy 2008, Editors: Luigi Ambrosio, Giuseppe Savaré
Authors
Series Title
C.I.M.E. Foundation Subseries
Series Volume
2028
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-21861-3
DOI
10.1007/978-3-642-21861-3
Softcover ISBN
978-3-642-21718-0
Edition Number
1
Number of Pages
XIII, 224
Number of Illustrations and Tables
1 b/w illustrations, 7 illustrations in colour
Topics