On continuity of minimizers for certain quadratic growth functionals

In this paper we treat the regularity problem for minimizers u ( x ) : Ω ⊂ R m → R n of quadratic growth functionals ∫ Ω A ( x , u , D u ) d x . About the dependence on the variable x we assume only that A ( ⋅ , u , p ) is in the class V M O as a function of x . Namely, we do not assume the continuity of A ( x , u , p ) with respect to x . We will prove a partial regularity result for the case m ≤ 4 .