Removable Sets for Weighted Orlicz-Sobolev Spaces

摘要

In this paper, we provide a concrete criterion for sets lying in a hyperplane to be removable for weighted Orlicz-Sobolev spaces. We define porous sets and show that the porous sets lying in a hyperplane are removable; this is a generalization of the results in Karak (Potential Anal 43(4):675-694, 2015), Futamura and Mizuta (Hiroshima Math J 33:43-57, 2003).