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. The
topics discussed are transport equations for nonsmooth vector
fields, homogenization, viscosity methods for the infinite
Laplacian, weak KAM theory and geometrical aspects of
symmetrization. A historical overview of all CIME courses on the
calculus of variations and partial differential equations is
contributed by Elvira Mascolo.
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