Calculus of Variations and Geometric Measure Theory
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Isoperimetric Problems Between Analysis and Geometry

Two characterizations of BV functions via semigroups in Euclidean and non–Euclidean spaces

Michele Jr Miranda

created by paolini on 02 Jun 2014

17 jun 2014 -- 11:00   [open in google calendar]

Abstract.

In this talk I shall survey some connections between the theory of semigroups and the theory of functions with bounded variation in Euclidean and non–Euclidean spaces. We shall focus our attention on two characterizations of functions of bounded variations; the first one dates from the early works of De Giorgi when the first definition and properties of functions with bounded variations and sets with finite perimeter in dimension more than one was given, the second one was suggested by Ledoux because of its connection with isoperimetric problem in Euclidean and Gaussian spaces. We shall see that these two approaches are still valid and sometimes necessary in the framework of Riemannian manifolds, metric measure spaces, Carnot groups and abstract Wiener spaces.

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