Imbedding estimates and elliptic equations with discontinuous coefficients in unbounded domain

Abstract

In this paper we deal with the multiplication operator<em> u ∈ W^{k,p} (Ω) → gu ∈ L^q (Ω),</em> with g belonging to a space of Morrey type. We apply our results in order to establish an a-priori bound for the solutions of the Dirichlet problem concerning elliptic equations with discontinuous coefficients.<br />