Global regularity in Orlicz-Morrey spaces of solutions to nondivergence elliptic equations with VMO coefficients

Abstract

We show continuity in generalized Orlicz-Morrey spaces M?,?(Rn) of sublinear integral operators generated by Calder´on-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 (Formula presented.) with discontinuous coefficients. We show that Lu ? M?, ? implies the second-order derivatives belong to M?,?. © 2018 Texas State University