Some Fine Properties of BV Functions on Wiener Spaces

Abstract

Abstract:In this paper we de ne jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the nite dimensional case. We also de ne the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.

Fractional Laplacians, perimeters and heat semigroups in Carnot groups

“…The aim of this paper is to define the fractional perimeter of a set in Carnot groups and to investigate some relations between fractional perimeter and the asymptotic behaviour of the fractional heat semigroup (i.e., the semigroup generated by the fractional Laplacian in L 2 ) as t → 0. Our results generalise those in [21,2,7,1], where semigroups generated by local elliptic operators are considered. We discuss in an informal way the case of R n in this introduction.…”

On integration by parts formula on open convex sets in Wiener spaces

“…Further, ∂Ω = (∂Ω ∩ C) ∪ N . Since Ω ⊂ C, we have N = ∂Ω ∩ ∂C, and by[8, Corollary 2.3] νΩ(x) = νC(x) for S ∞−1 -a.e. x ∈ ∂Ω ∩ ∂C.…”

On integration by parts formula on open convex sets in Wiener spaces

“…where we still denote by f a representative of f , since (i), (ii) and (iii) follow from (8). We consider…”