Calculus of Variations and Partial Differential Equations

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Calculus of variations is a major branch of analysis, and partial differential equations are used to model natural phenomena and are used in all of the physical sciences. Using degree theory and the geometric problem of evolution of a surface, this text brings these two fields together.At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.