Regularity and well posedness for the Laplace operator on polyhedral   domains
  We announce a well-posedness result for the Laplace equation in weighted Sobolev spaces on polyhedral domains in $\RR^n$ with Dirichlet boundary conditions. The weight is the distance to the set of singular boundary points. We give a detailed sketch of the proof in three dimensions. 
Constantin Bacuta, Victor Nistor, Ludmil Zikatanov