Calculus of Variations and Geometric Measure Theory
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D. Addona - G. Menegatti - M. Miranda Jr

Characterization of BV functions on open domains: the Gaussian case and the general case

created by addona on 12 Mar 2019

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Inserted: 12 mar 2019
Last Updated: 12 mar 2019

Year: 2019

Abstract:

We provide three different characterizations of the space $BV(O,\gamma)$ of the functions of bounded variation with respect to a centred non-degenerate Gaussian measure $ \gamma$ on open domains $O$ in Wiener spaces. Throughout these different characterizations we deduce a sufficient condition for belonging to $BV(O,\gamma)$ by means of the Ornstein-Uhlenbeck semigroup and we provide an explicit formula for one-dimensional sections of functions of bounded variation. Finally, we apply our technique to Fomin differentiable probability measures $\nu$ on a Hilbert space $X$, inferring a characterization of the space $BV(O,\nu)$ of the functions of bounded variation with respect to $\nu$ on open domains $O\subseteq X$.


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