A density result on Orlicz-Sobolev spaces in the plane

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 $\Psi$.

11 pages, 1 figure