Bounded Approximation Property for Sobolev spaces on simply-connected   planar domains
  We show that Sobolev space $W^1_1(\Omega)$ of any planar one-connected domain $\Omega$ has the Bounded Approximation property. The result holds independently from the properties of the boundary of $\Omega$. The prove is based on a new decomposition of a planar domain. 
Maria Roginskaya, Michal Wojciechowski
math.FA math.MG