Hostname: page-component-7dd5485656-hw7sx Total loading time: 0 Render date: 2025-10-30T17:41:45.208Z Has data issue: false hasContentIssue false
  • English
  • Français

On Korn's first inequality with non-constant coefficients

Published online by Cambridge University Press:  12 July 2007

Patrizio Neff
Patrizio Neff
Affiliation:
AG6, Fachbereich Mathematik, Technische Universitaet Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany/Allemagne (neff@mathematik.tu-darmstadt.de)
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we prove a Korn-type inequality with non-constant coefficients which arises from applications in elasto-plasticity at large deformations. More precisely, let Ω ⊂ R3 be a bounded Lipschitz domain and let Γ ⊂ ∂Ω be a smooth part of the boundary with non-vanishing two-dimensional Lebesgue measure. Define and let be given with det Fp(x) ≥ μ+ > 0. Moreover, suppose that Rot . Then Clearly, this result generalizes the classical Korn's first inequalitywhich is just our result with Fp = 11. With slight modifications, we are also able to treat forms of the type

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 1 , February 2002 , pp. 221 - 243
Copyright
Copyright © Royal Society of Edinburgh 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable