Evolution Problems and Minimizing Movements
We recall the definition of Minimizing Movements, suggested by E. De Giorgi, and we consider some applications to evolution problems. With regards to ordinary differential equations, we prove in particular a generalization of maximal slope curves theory to arbitrary metric spaces. On the other hand we present a unifying framework in which some recent conjectures about partial differential equations can be treated and solved. At the end we consider some open problems.