Removable sets in elliptic equations with Musielak-Orlicz growth

Abstract

We characterize, in the terms of intrinsic Hausdorff measures, the size of~removable sets for Hölder continuous solutions to elliptic equations with Musielak-Orlicz growth. In the general case we provide an elegant form of the measure that captures -- as special cases -- the classical results, slightly refines the ones provided for problems stated in the variable exponent and double phase spaces and essentially improves the known one in the Orlicz case.

the manuscript extends arXiv:1901.03412 to the general growth