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

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.

List 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.

Product details

• Authors: Stefano Bianchini, Eric A. Carlen, Alexander Mielke, Cédric Villani
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 30.07.2011
• EAN: 9783642217180
• ISBN: 978-3-642-21718-0
• No. of pages: 224
• Dimensions: 158 mm x 12 mm x 234 mm
• Weight: 387 g
• Illustrations: XIII, 224 p. 8 illus., 7 illus. in color.
• Series: Lecture Notes in Mathematics; C.I.M.E. Foundation Subseries
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Analysis, B, Optimization, Mathematics and Statistics, Functional Analysis, Differential Geometry, Partial Differential Equations, Differential calculus & equations, Calculus of Variations and Optimization, Calculus of variations, Calculus of Variations and Optimal Control; Optimization, Analysis (Mathematics), Functional analysis & transforms, Mathematical analysis, Differential & Riemannian geometry