Inserted: 5 feb 2012
Last Updated: 7 dec 2013
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