Stability and Continuity of Functions of Least Gradient

H. Hakkarainen ; R. Korte ; P. Lahti ; N. Shanmugalingam

Analysis and Geometry in Metric Spaces, Tome 3 (2015), / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2015-01-01

Zbl 1318.26028

EUDML-ID : urn:eudml:doc:271003

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