Calculus of Variations and Nonlinear Partial Differential Equations : With a historical overview by Elvira Mascolo

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. Front Matter....Pages I-XI Transport Equation and Cauchy Problem for Non-Smooth Vector Fields....Pages 1-41 Issues in Homogenization for Problems with Non Divergence Structure....Pages 43-74 A Visit with the ∞-Laplace Equation....Pages 75-122 Weak KAM Theory and Partial Differential Equations....Pages 123-154 Geometrical Aspects of Symmetrization....Pages 155-181 CIME Courses on Partial Differential Equations and Calculus of Variations....Pages 183-189 Back Matter....Pages 193-204 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. Luigi Ambrosio ... [et Al.] ; With A Historical Overview By Elvira Mascolo ; Editors, Bernard Dacorogna, Paolo Marcellini. Includes Bibliographical References.