Holder continuity for vector-valued minimizers of quadratic functionals

Abstract

In this article we give a sufficient condition for interior everywhere Hölder continuity of weak minimizers of a class of quadratic functionals with coefficients Aαβ ij(‧, u) belonging to the VMO-class, uniformly with respect to u ∈ ℝN, and continuous with respect to u. The condition is global. It is typical for the functionals belonging to the class that the continuity moduli of their coefficients become slowly growing sufficiently far from zero. Some features of the main result are illustrated by examples.