Global H?lder continuity of weak solutions to quasilinear divergence form elliptic equations

摘要

We derive global H?lder regularity for the W_0~(1, 2) (Ω)-weak solutions to the quasilinear, uniformly elliptic equationdiv (a~(i j) (x, u) D_j u + a~i (x, u)) + a (x, u, D u) = 0 over a C~1-smooth domain Ω ? R~n, n ≥ 2. The nonlinear terms are all of Carathéodory type with coefficients a~(i j) (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, D u) exhibit controlled growths with respect to u and the gradient Du.