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

Abstract

We use a new combinatorial technique to prove the optimal interior partial regularity result for L p-vector fields with integer fluxes that minimize the L p-energy. More precisely, we prove that the minimizing vector fields are Holder continuous outside a set that is locally finite inside the domain. The results continue the program started in [25], but this paper is self-contained.