BV functions on convex domains in Wiener spaces. (English) Zbl 1321.28027
The authors summarize the contents of this paper in the abstract and introduction of the paper as follows: This paper is devoted to bounded variation (BV) functions in open sets of infinite dimensional separable Banach spaces endowed with Gaussian measures. BV functions defined in the whole space \(X\) have been introduced in [M. Fukushima, J. Funct. Anal. 174, No. 1, 227–249 (2000; Zbl 0978.60088)] and studied also in [L. Ambrosio et al., J. Funct. Anal. 258, No. 3, 785–813 (2010; Zbl 1194.46066)], [M. Fukushima and M. Hino, J. Funct. Anal. 183, No. 1, 245–268 (2001; Zbl 0993.60049)]. As in the finite dimensional case, they are strongly related to geometric measure theory and in particular to the theory of perimeters. In fact, they study functions of bounded variation defined in an abstract Wiener space \(X\), relating the variation of a function u on a convex open set \(\Omega \subset X\) to the behavior near \(t=0\) of \(T(t)u\), \(T(t)\) being the Ornstein-Uhlenbeck semigroup in \(\Omega\).
Reviewer: Kun Soo Chang (Seoul)
MSC:
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
| 26B30 | Absolutely continuous real functions of several variables, functions of bounded variation |
| 47D07 | Markov semigroups and applications to diffusion processes |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
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