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 $${\varOmega }\subseteq X$$ Ω ⊆ X , X being an infinite-dimensional separable 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.