Characterizations of sets of finite perimeter using heat kernels in metric spaces
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 $1$Poincaré 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 ${\rm BV}$ functions in terms of a neardiagonal energy in this general setting.
 Publication:

arXiv eprints
 Pub Date:
 May 2014
 arXiv:
 arXiv:1405.0186
 Bibcode:
 2014arXiv1405.0186M
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 To appear in Potential Analysis