Dirichlet boundary value problems for uniformly elliptic equations in modified local generalized Sobolev–Morrey spaces

摘要

In this paper, we study the boundedness of the sublinear operators, generated by Calderón–Zygmund operators in local generalized Morrey spaces. By usingthese results we prove the solvability of the Dirichlet boundary value problem for apolyharmonic equation in modified local generalized Sobolev–Morrey spaces. We obtain a priori estimates for the solutions of the Dirichlet boundary value problems forthe uniformly elliptic equations in modified local generalized Sobolev–Morrey spacesdefined on bounded smooth domains.