Removable sets for Orlicz-Sobolev spaces

TL;DR

This paper investigates the conditions under which certain porous sets are removable for Orlicz-Sobolev spaces characterized by specific growth functions, establishing sharp criteria for removability.

Contribution

It provides a characterization of removable sets for Orlicz-Sobolev spaces with logarithmic growth, extending previous results to a broader class of functions.

Findings

$(p,\lambda)$-porous sets in a hyperplane are removable

The results are essentially sharp, indicating optimal conditions

Extends the theory of removable sets to Orlicz-Sobolev spaces with logarithmic growth

Abstract

We study removable sets for the Orlicz-Sobolev space $W^{1,\Psi},$ for functions of the form $\Psi(t)=t^p\log^{\lambda}(e+t).$ We show that $(p,\lambda)$-porous sets lying in a hyperplane are removable and that this result is essentially sharp.