Gradient flow for the one-dimensional Mumford-Shah functional
Non-local approximation of functionals: variational and evolution problems
Questa nota tratta dell'approssimazione di funzionali, usati in problemi con discontinuità libere, mediante famiglie di funzionali non locali in cui il gradiente è sostituito dal rapporto incrementale. Vengono inoltre presentate alcune applicazioni di questa teoria a problemi variazionali e di evoluzione.
Unstable simple modes for a class of Kirchhoff equations
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.
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