Weighted Sobolev spaces and regularity for polyhedral domains

Bernd Ammann; Victor Nistor

doi:10.1016/j.cma.2006.10.022

Weighted Sobolev spaces and regularity for polyhedral domains

Bernd Ammann, Victor Nistor

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We prove a regularity result for the Poisson problem - Δ u = f, u |_{∂ P} = g on a polyhedral domain P ⊂ R³ using the Babuška-Kondratiev spaces K_a^m (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 K_a^m-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 K_a^m (P).

Original language	English (US)
Pages (from-to)	3650-3659
Number of pages	10
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	196
Issue number	37-40 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.cma.2006.10.022
State	Published - Aug 1 2007

All Science Journal Classification (ASJC) codes

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/j.cma.2006.10.022

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T1 - Weighted Sobolev spaces and regularity for polyhedral domains

AU - Ammann, Bernd

AU - Nistor, Victor

PY - 2007/8/1

Y1 - 2007/8/1

N2 - We prove a regularity result for the Poisson problem - Δ u = f, u |∂ P = g on a polyhedral domain P ⊂ 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 [4,33]. 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).

AB - We prove a regularity result for the Poisson problem - Δ u = f, u |∂ P = g on a polyhedral domain P ⊂ 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 [4,33]. 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).

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DO - 10.1016/j.cma.2006.10.022

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JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 37-40 SPEC. ISS.

ER -

Weighted Sobolev spaces and regularity for polyhedral domains

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