Two characterization of BV functions on Carnot groups via the heat semigroup
Analysis of PDEs
2011-07-21 v1 Functional Analysis
Abstract
In this paper we provide two different characterizations of sets with finite perimeter and functions of bounded variation in Carnot groups, analogous to those which hold in Euclidean spaces, in terms of the short-time behaviour of the heat semigroup. The second one holds under the hypothesis that the reduced boundary of a set of finite perimeter is rectifiable, a result that presently is known in Step 2 Carnot groups.
Keywords
Cite
@article{arxiv.1107.3996,
title = {Two characterization of BV functions on Carnot groups via the heat semigroup},
author = {Marco Bramanti and Michele Miranda and Diego Pallara},
journal= {arXiv preprint arXiv:1107.3996},
year = {2011}
}