Calculus of Variations and Geometric Measure Theory

N. Marola - M. Miranda Jr - N. Shanmugalingam

Characterizations of sets of finite perimeter using heat kernels in metric spaces

created by miranda on 29 Apr 2014
modified by shanmugal on 27 Apr 2016


Online First Paper

Inserted: 29 apr 2014
Last Updated: 27 apr 2016

Journal: Potential Analysis
Year: 2016
Doi: 10.1007/s11118-016-9560-3


The overarching goal of this paper is to link the notion of sets of finite perimeter (a concept associated with $N^{1,1}$-spaces) and the theory of heat semigroups (a concept related to $N^{1,2}$-spaces) in the setting of metric measure spaces whose measure is doubling and supports a $1$-Poincar ́e inequality. We prove a characterization of sets of finite perimeter in terms of a short time behavior of the heat semigroup in such metric spaces. We also give a new characterization of $BV$ functions in terms of a near-diagonal energy in this general setting.