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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)
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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 inequality which is just our result with Fp = 11. With slight modifications, we are also able to treat forms of the type

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

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