Evolution problems and minimizing movements
In the paper E. De Giorgi's ideas of MM (``minimizing movements'') and of GMM (``generalized minimizing movements'') are developed in two directions. First, in connection with ODE's, various problems concerning the interrelations between the MM, GMM and the solution sets to the Cauchy problem for gradient type differential equations are considered. Also in this part, the authors present some generalization to the case of arbitrary metric spaces of the theory of maximal slope curves developed in Hilbert spaces by E. De Giorgi, A. Marino, M. Tosques, M. Degiovanni, C. Saccon,\dots. Second, in the domain of PDE's the authors present an unified framework for formulating and solving some recent conjectures of De Giorgi concerning the parabolic equations and minimizing movements in Hilbert or in uniformly convex Banach spaces. Some open problems, concerning for instance the regularity or semigroup property, for MM or GMM are also formulated.
scientific article; zbMATH DE number 766465