Weighted Sobolev spaces and regularity for polyhedral domains Original Research Article

We prove a regularity result for the Poisson problem image, image on a polyhedral domain image using the Babuška–Kondratiev spaces image. These are weighted Sobolev spaces in which the weight is given by the distance to the set of edges . In particular, we show that there is no loss of image—regularity for solutions of strongly elliptic systems with smooth coefficients. We also establish a “trace theorem” for the restriction to the boundary of the functions in image.