La teoria dei perimetri di Caccioppoli–De Giorgi e i suoi più recenti sviluppi

Abstract

In this paper we illustrate the theory of sets of finite perimeter, starting from the pioneering intuitions of Caccioppoli and De Giorgi’s seminal papers. In the second part of the paper we illustrate some more recent developments and open problems in metric measure spaces, in Carnot groups and in infinite-dimensional Gaussian spaces.