Dominik Schlagenhauf

A Discontinuous Solution of the Critical n-Laplace System with Antisymmetric Potential

Let $n>2$. We construct a map $U\in W^{1,n}(B^n,\mathbb{R}^{n+2})$ that is discontinuous at the origin and smooth on the punctured ball $B^n \setminus \{0\}$, together with an antisymmetric potential $\Omega\in L^n(B^n,so(n+2)\otimes\mathbb{R}^n)$ such that $-\mathrm{Div}(|\nabla U|^{n-2}\nabla U)=\Omega\cdot |\nabla U...