Luis A. Caffarelli

This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L. C. Evans, N. Fusco at the Summer course held in Cetraro, Italy in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. Coverage includes transport equations for nonsmooth vector fields, viscosity methods for the infinite Laplacian, and geometrical aspects of symmetrization.

Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.

Presents a self-contained development of the regularity theory for solutions of fully nonlinear elliptic equations. This book describes various techniques that are needed to extend the classical Schauder and Calderon-Zygmund regularity theories for linear elliptic equations to the fully nonlinear context.