Asymptotics in a neighborhood of infinity of solutions with finite Dirichlet integral of second-order elliptic equations

Abstract

In this paper we answer a question posed by E. Sanchez-Palencia which arose in the theory of homogenization of differential operators. The asymptotic behavior of solutions at infinity which have finite Dirichlet integral is studied and uniqueness theorems are also proved for exterior boundary problems for second-order elliptic equations in divergent form.