Regularity result for nondivergence equations with unbounded coefficients

Abstract

The aim of this paper is to establish a higher integrability result for the second derivatives of solutions to nondivergence elliptic equations of the type $\sum_{i,j}^n a_{ij} \frac{\partial^2 u}{\partial x_i \partial x_j} =h$. The matrix coefficient $A(x)=[a_{ij}(x)]_{ij}$ is assumed to belong to the space $BMO$.