On continuity of minimizers for certain quadratic growth functionals

摘要

In this paper we treat the regularity problem for minimizers u(x) : Ω is contained in R~m → R~n of quadratic growth functionals ∫_Ω A(x, u, Du)dx. About the dependence on the variable x we assume only that A(·,u,p) is in the class V MO 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.