Weighted Sobolev spaces and regularity for polyhedral domains

Bernd Ammann (1) , Victor Nistor (2)

1 IECN - Institut Élie Cartan de Nancy
2 Penn State - Pennsylvania State University

We prove a regularity result for the Poisson problem $-\Delta u = f$, $u \vert_{\pa \PP} = g$ on a polyhedral domain $\PP \subset \RR^3$ using the \BK\ spaces $\Kond{m}{a}(\PP)$. These are weighted Sobolev spaces in which the weight is given by the distance to the set of edges \cite{Babu70, Kondratiev67}. In particular, we show that there is no loss of $\Kond{m}{a}$--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 $\Kond{m}{a}(\PP)$.

Mots clés: non-smooth boundary; regularity

Domaines: Equations aux dérivées partielles [math.AP]

Bernd Ammann, Victor Nistor. Weighted Sobolev spaces and regularity for polyhedral domains. 2006. ⟨hal-00090987⟩