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 shorttime behaviour of the semigroup associated with a perturbation of the OrnsteinUhlenbeck operator.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.07181
 Bibcode:
 2020arXiv200607181A
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Analysis of PDEs;
 28C20