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Weighted Sobolev spaces and regularity for polyhedral domains

Bernd Ammann·Victor Nistor
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Abstract

We prove a regularity result for the Poisson problem $-Δu = f$, $u |\_{\pa \PP} = g$ 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 $\Kond{m}{a}(\PP)$.

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Bernd Ammann, Victor Nistor. 2015-10-27. Weighted Sobolev spaces and regularity for polyhedral domains. https://doi.org/10.1016/j.cma.2006.10.022

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