Titlebook: Calculus of Variations and Nonlinear Partial Differential Equations; Lectures given at th Luigi Ambrosio,Luis Caffarelli,Nicola Fusco,Berna

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0075-8434 . 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, visc

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Lecture Notes in Computer Scienceferential equations is known as homogenization. The effect of the inhomogeneities oscillating at small scales is often not a simple average and may be hard to predict: a geodesic in an irregular medium will try to avoid the bad areas, the roughness of a surface may affect in nontrivial way the shapes of drops laying on it, etc…

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Issues in Homogenization for Problems with Non Divergence Structure,ferential equations is known as homogenization. The effect of the inhomogeneities oscillating at small scales is often not a simple average and may be hard to predict: a geodesic in an irregular medium will try to avoid the bad areas, the roughness of a surface may affect in nontrivial way the shapes of drops laying on it, etc…

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Weak KAM Theory and Partial Differential Equations, third CIME course I have given during the past ten years, the others at the meetings on “Viscosity solutions and applications” (Montecatini Terme, 1995) and on “Optimal transportation and applications” (Martina Franca, 2001).

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Book 2008l 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..