Calculus of Variations and Geometric Measure Theory
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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

[BibTeX]

Online First Paper

Inserted: 29 apr 2014
Last Updated: 27 apr 2016

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

Abstract:

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.


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