A density result for homogeneous Sobolev spaces on planar domains

Abstract

We show that in a bounded simply connected planar domain $\Omega$ the smooth Sobolev functions $W^{k,\infty }(\Omega )\cap C^{\infty }(\Omega )$ are dense in the homogeneous Sobolev spaces $L^{k,p}(\Omega )$.

17 pages, 4 figures