A density result for homogeneous Sobolev spaces on planar domains (1801.02824v1)

Published 9 Jan 2018 in math.FA and math.CA

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 $L^{{k,p}(\Omega)$.}