Sublinear Elliptic Equations with Unbounded Coefficients in Lipschitz Domains

Abstract

This paper is concerned with the homogeneous Dirichlet problem for a sublinear elliptic equation with unbounded coefficients in a Lipschitz domain. Bilateral a priori estimates for positive solutions and a priori upper estimates for their gradients are presented as a byproduct of the boundary Harnack principle. These estimates allow us to show the uniqueness of a positive solution of the homogeneous Dirichlet problem under no information about normal derivatives unlike in smooth domains.