Ein Regularitätssatz für ein lineares System von Variationsungleichungen mit einer Halbraumnebenbedingung

Abstract

We consider linear non-diagonal elliptic systems of variational inequalities where the admissible class of functions is characterized by Dirichlet boundary conditions and a half-space constraint $u\cdot a\ge \theta$ for some fixed vector $a\in {\mathbb{R}}^n$. By potential theoretic arguments we show continuity of the solution provided the obstacle $\theta :\Omega \to \mathbb{R}$ is a continuous function.