Interior partial regularity for minimal Lp-vectorfields with integer fluxes

Abstract

We use a new combinatorial technique to prove the optimal interior partial regularity result for Lp-vectorfields with integer fluxes minimizing the Lp-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 collaboration with Tristan Rivière, but this paper is self-contained.

36 pages, 6 figures. Some typos corrected, style made more fluent, improved end of proof p. 18-19