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arXiv · 2006.07181

On functions of bounded variation on convex domains in Hilbert spaces

L. Angiuli·S. Ferrari·D. Pallara
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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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L. Angiuli, S. Ferrari, D. Pallara. 2020-06-12. On functions of bounded variation on convex domains in Hilbert spaces. https://doi.org/10.1007/s00028-021-00680-8

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