Compactness methods for Hölder estimates of certain degenerate elliptic equations

Abstract

In this paper we obtain the interior $C^{1,\alpha}$ regularity of the quasilinear elliptic equations of divergence form. Our basic tools are the elementary local $L^\infty$ estimates and weak Harnack inequality for second-order linear elliptic equations, and the compactness method.

Keywords

• hölder estimates
• degenerate
• elliptic
• compactness method