On functions of bounded variation on convex domains in Hilbert spaces

Abstract

We study functions of bounded variation (and sets of finite perimeter) on a convex open set $\Omega \subseteq X$, $X$ being an infinite dimensional real Hilbert space. We relate the total variation of such functions, defined through an integration by parts formula, to the short-time behaviour of the semigroup associated with a perturbation of the Ornstein--Uhlenbeck operator.

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