Global Regularıty In Orlıcz-Morrey Spaces Of Solutıons To Nondıvergence Ellıptıc Equatıons Wıth Vmo Coeffıcıents

Abstract

We show continuity in generalized Orlicz-Morrey spaces M-Phi,M-phi (R-n) of sublinear integral operators generated by Calderon-Zygmund operator and their commutators with BMO functions. The obtained estimates are used to study global regularity of the solution of the Dirichlet problem for linear uniformly elliptic operator L = Sigma(3)(i,j=1) a(ij)(x)D-ij with discontinuous coefficients. We show that Lu is an element of M-Phi,M-phi implies the second-order derivatives belong to M-Phi,M-phi.