# Weighted Sobolev spaces and regularity for polyhedral domains

by

Bernd Ammann, Victor Nistor

**Weighted Sobolev spaces and regularity for polyhedral domains**
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*Comput. Methods Appl. Mech. Engrg.* **196**
*3650-3659* (2007)

DOI: 10.1016/j.cma.2006.10.022

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. 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 $\Kond{m}{a}(\PP)$.

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The Paper was written on 1.12.2005

Last update 9.6.2006