Removable sets for weighted Orlicz-Sobolev spaces

TL;DR

This paper investigates the properties of removable sets within weighted Orlicz-Sobolev spaces, extending the concept of porous sets and demonstrating their removability when contained in a hyperplane.

Contribution

It generalizes the notion of porous sets and establishes their removability in weighted Orlicz-Sobolev spaces, broadening understanding of set removability in these function spaces.

Findings

Porous sets in a hyperplane are removable in weighted Orlicz-Sobolev spaces.

Generalization of porous sets concept to weighted Orlicz-Sobolev spaces.

Extension of removability criteria for sets in advanced function spaces.

Abstract

The aim in the present paper is to study removable sets for weighted Orlicz-Sobolev spaces. We generalize the definition of porous sets and show that the porous sets lying in a hyperplane are removable.