Weighted Sobolev spaces and regularity for polyhedral domains

We prove a regularity result for the Poisson problem -Δu=f-Δu=f, u|∂P=gu|∂P=g on a polyhedral domain P⊂R3P⊂R3 using the Babuška–Kondratiev spaces Kam(P). These are weighted Sobolev spaces in which the weight is given by the distance to the set of edges [4] and [33]. In particular, we show that there is no loss of Kam—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 Kam(P).