Existence and uniqueness of solutions to outer Zaremba problem for elliptic equations with measure-valued potential

Abstract

In the exterior of a ball in the space $\mathbb{R}^n$ we consider the Zaremba and Neumann problems for quasilinear second order elliptic problems with a measure-valued potential. We proved the existence and uniqueness of entropy solution to the Zaremba and Neumann problems.