A density result on Orlicz-Sobolev spaces in the plane

TL;DR

This paper proves that smooth functions are dense in Orlicz-Sobolev spaces on bounded simply connected planar domains, extending classical density results to more general function spaces.

Contribution

It establishes the density of smooth Sobolev functions in Orlicz-Sobolev spaces for specific planar domains and Young functions, generalizing known results.

Findings

Smooth functions are dense in $L^{k, ext{ extPhi}}( ext{ extOmega})$ for the specified setting.

The result applies to bounded simply connected planar domains and doubling Young functions.

This extends classical Sobolev density results to Orlicz-Sobolev spaces.

Abstract

We show the density of smooth Sobolev functions $W^{k,\infty}(\Omega)\cap C^\infty(\Omega)$ in the Orlicz-Sobolev spaces $L^{k,\Psi}(\Omega)$ for bounded simply connected planar domains $\Omega$ and doubling Young functions $\Psi$.