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.

Offers an exposition on free boundary problems. Free or moving boundary problems appear in many areas of analysis, geometry, and applied mathematics. This book is useful for supplementary reading or as an independent study text. It is also suitable for gra