Partial regularity for elliptic systems with critical growth

Abstract

We prove a partial Hölder regularity result for weak solutions $u:\Omega \to {\mathbb{R}}^N$, $N\ge 2$, to non-autonomous elliptic systems with general growth of the type

The crucial point is that the operator $a$ satisfies very weak regularity properties and general growth, while for the inhomogeneity $b$ we allow a critical growth condition.