Global regularity for solutions of a class of quasilinear elliptic equations

We derive interior and global Hölder estimates for solutions of a class of quasilinear elliptic equations. First, the interior Hölder continuity is obtained by the iteration of an oscillation estimate. Then, the Hölder continuity up to the boundary is established in domains with certain boundary constraints. Last, we prove the global Hölder continuity of solutions provided that their restrictions on boundary are Hölder continuous. The concluding section presents an application to illustrate our main results.