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

We derive global Hölder regularity for the W01,2(Ω)-weak solutions to the quasilinear, uniformly elliptic equationdiv(aij(x,u)Dju+ai(x,u))+a(x,u,Du)=0 over a C1-smooth domain Ω⊂Rn, n⩾2. The nonlinear terms are all of Carathéodory type with coefficients aij(x,u) belonging to the class VMO of functions with vanishing mean oscillation with respect to x, while ai(x,u) and a(x,u,Du) exhibit controlled growths with respect to u and the gradient Du.