Calculus of Variations and Geometric Measure Theory
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M. Bramanti - M. Miranda Jr - D. Pallara

Two characterization of BV functions on Carnot groups via the heat semigroup

created by pallara on 04 Nov 2010
modified by miranda on 16 Nov 2012


Published Paper

Inserted: 4 nov 2010
Last Updated: 16 nov 2012

Journal: Int. Math. Res. Notices
Volume: 17
Pages: 3845--3876
Year: 2012


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.


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