Calculus of Variations and Geometric Measure Theory
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M. Petrache

Interior partial regularity for minimal $L^p$-vectorfields with integer fluxes

created by petrache on 05 Feb 2012
modified on 07 Dec 2013


Accepted Paper

Inserted: 5 feb 2012
Last Updated: 7 dec 2013

Year: 2012


We use a new combinatorial technique to prove the optimal interior partial regularity result for $L^p$-vectorfields with integer fluxes minimizing the $L^p$-energy. More precisely, we prove that the minimal vectorfields are Hölder outside a set which is locally finite inside the domain. The results continue the program started in previous work with Tristan Rivière but this paper is self-contained.

Keywords: vectorfields with integer fluxes, topological singularities, regularity theory


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