Stability and continuity of functions of least gradient
Abstract
In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develop some stability properties of sequences of least gradient functions. We also apply these tools to prove a maximum principle for functions of least gradient that arise as solutions to a Dirichlet problem.
 Publication:

arXiv eprints
 Pub Date:
 October 2014
 arXiv:
 arXiv:1410.2228
 Bibcode:
 2014arXiv1410.2228H
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Analysis of PDEs;
 Mathematics  Optimization and Control;
 Primary 26B30;
 Secondary 31E99;
 31C45;
 26B15
 EPrint:
 29 pages