Accessible Unlicensed Requires Authentication Published by De Gruyter February 25, 2014

Regularity of minimizers of the area functional in metric spaces

Heikki Hakkarainen, Juha Kinnunen and Panu Lahti

Abstract

In this article we study minimizers of functionals of linear growth in metric measure spaces. We introduce the generalized problem in this setting, and prove existence and local boundedness of the minimizers. We give counterexamples to show that in general, minimizers are not continuous and can have jump discontinuities inside the domain.

Funding source: Academy of Finland

Funding source: Väisälä Foundation

Received: 2013-9-25
Revised: 2014-2-3
Accepted: 2014-2-11
Published Online: 2014-2-25
Published in Print: 2015-1-1

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