Weighted sobolev spaces and regularity for polyhedral domains

Dedicated to Ivo Babuška on the occasion of his 80th birthday. Abstract. We prove a regularity result for the Poisson problem −∆u = f, u|∂P = g on a polyhedral domain P ⊂ R3 using the Babuška–Kondratiev spaces Kma (P). These are weighted Sobolev spaces in which the weight is given by the distance to the set of edges [4, 33]. In particular, we show that there is no loss of Kma –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 Kma (P). Content