Global Hölder continuity of weak solutions to quasilinear divergence form elliptic equations

We derive global Holder regularity for the W(0)(1,2)(Omega)-weak solutions to the quasilinear, uniformly elliptic equation div(a(ij)(x, u)D(j)u + a(i)(x, u)) + a(x, u, Du) = 0 over a C(1)-smooth domain Omega subset of R(n), n >= 2. The nonlinear terms are all of Caratheodory type with coefficients a(ij)(x, u) belonging to the class VMO of functions with vanishing mean oscillation with respect to x, while a(i)(x, u) and a(x, u, Du) exhibit controlled growths with respect to u and the gradient Du. (C) 2009 Elsevier Inc. All rights reserved.