A density result on Orlicz-Sobolev spaces in the plane

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