Interior partial regularity for minimal Lp-vectorfields with integer fluxes

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.

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