TY - BOOK ID - 107628081 TI - Nonlinear PDE's and Applications : C.I.M.E. Summer School, Cetraro, Italy 2008, Editors: Luigi Ambrosio, Giuseppe Savaré AU - Bianchini, Stefano AU - Carlen, Eric A AU - Mielke, Alexander AU - Villani, Cédric AU - SpringerLink (Online service) PY - 2011 SN - 9783642218613 PB - Berlin Heidelberg Springer Berlin Heidelberg Imprint Springer DB - UniCat KW - Differential geometry. Global analysis KW - Functional analysis KW - Partial differential equations KW - Mathematical analysis KW - Numerical methods of optimisation KW - differentiaalvergelijkingen KW - analyse (wiskunde) KW - differentiaal geometrie KW - functies (wiskunde) KW - kansrekening KW - optimalisatie UR - https://www.unicat.be/uniCat?func=search&query=sysid:107628081 AB - 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. ER -