Schauder type estimates for degenerate or singular elliptic equations with DMO coefficients

Abstract

In this paper, we study degenerate or singular elliptic equations in divergence form $$-\text{div}(x_n^{\hat{I}}\pm A\nabla u)=\text{div}(x_n^{\hat{I}}\pm \mathbf{g})\text{in }{B}_1\cap \{x_n>0\}.$$ When $\hat{I}\pm >-1$, we establish boundary Schauder type estimates under the conormal boundary condition on the flat boundary, provided that the coefficients satisfy Dini mean oscillation (DMO) type conditions. Additionally, as an application, we derive higher-order boundary Harnack principles for uniformly elliptic equations in divergence form with DMO coefficients.

41 pages