Weighted Sobolev spaces and regularity for polyhedral domains

Bernd Ammann, Victor Nistor

Research output: Contribution to journalArticle

12 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 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).

Original languageEnglish (US)
Pages (from-to)3650-3659
Number of pages10
JournalComputer Methods in Applied Mechanics and Engineering
Volume196
Issue number37-40 SPEC. ISS.
DOIs
StatePublished - Aug 1 2007

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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