Conservation Laws for $p$-Harmonic Systems with Antisymmetric Potentials and Applications

Abstract

We prove that $p $-harmonic systems with antisymmetric potentials can be written in divergence form as a conservation law. This extends to the $p$-harmonic framework the original work from 2006 of the second author for $p=2$ (arXiv:math/0603380). We give applications of the existence of this divergence structure in the analysis $p\rightarrow 2$.