Global Morrey regularity for asymptotically regular elliptic equations

Abstract

We establish the global Morrey regularity and continuity results for solutions to nonlinear elliptic equations over bounded nonsmooth domains. The novelty of our contribution is that the principal part of the operator is assumed to be merely asymptotically regular with respect to the gradient of a solution, which means that it behaves like the p-Laplacian operator for large values, while the lower order terms satisfy controlled growth conditions with respect to variables modeled by the functions from Morrey spaces. Our results extend to a larger class of degenerate and singular elliptic equations from by now regular problems in the literature. (C) 2017 Elsevier Ltd. All rights reserved.