Another Approach of Morrey Estimate for Linear Elliptic Equations with Partially BMO Coefficients in a Half Space

Abstract

Making use of an elementary approach instead of the weighted $L^p$ estimate with a special weight, we prove global Morrey estimates of the weak derivatives to the Dirichlet problems of linear elliptic equations with small partially  BMO coefficients in a half space. Here, the leading coefficients $a^{ij}(x)$ are assumed to be merely measurable in one variable, and have small BMO in the remaining spatial variables.