Well-posedness and regularity for the elasticity equation with mixed boundary conditions on polyhedral domains and domains with cracks

Anna L. Mazzucato, Victor Nistor

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

We prove a regularity result for the anisotropic linear elasticity equation Pu:= div(C. ∇u) = f, with mixed (displacement and traction) boundary conditions on a curved polyhedral domain Ω ⊂ ℝ3 in weighted Sobolev spaces Km+1a=1 (Ω), for which the weight is given by the distance to the set of edges. In particular, we show that there is no loss of Kma-regularity. Our curved polyhedral domains are allowed to have cracks. We establish a well-posedness result when there are no neighboring traction boundary conditions and {combining long vertical line overlay}a{combining long vertical line overlay} < η, for some small η > 0 that depends on P, on the boundary conditions, and on the domain Ω. Our results extend to other strongly elliptic systems and higher dimensions.

Original languageEnglish (US)
Pages (from-to)25-73
Number of pages49
JournalArchive for Rational Mechanics and Analysis
Volume195
Issue number1
DOIs
StatePublished - Oct 1 2009

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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