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Title: Korn's inequality uniform with respect to a class of axisymmetric bodies (English)
Author: Hlaváček, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 34
Issue: 2
Year: 1989
Pages: 146-154
Summary lang: English
Category: math
Summary: The Korn's inequality involves a positive constant, which depends on the domains, in general. We prove that the constants have a positive infimum, if a class of bounded axisymmetric domains and axisymmetric displacement fields are considered. (English)
Keyword: domain optimization
Keyword: shape optimization
Keyword: Korn’s inequality
MSC: 35J55
MSC: 49A22
MSC: 49J20
MSC: 73C99
MSC: 73k40
MSC: 74B99
idZBL: Zbl 0673.49004
idMR: MR0990301
DOI: 10.21136/AM.1989.104342
Date available: 2008-05-20T18:36:21Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] J. Haslinger P. Neittaanmäki T. Tiihonen: Shape optimization of an elastic body in contact based on penalization of the state.Apl. Mat. 31 (1986), 54-77. MR 0836802
Reference: [2] I. Hlaváček: Inequalities of Korn's type, uniform with respect to a class of domains.Apl. Mat. Zbl 0673.49003
Reference: [3] I. Hlaváček: Domain optimization in axisymmetric elliptic boundary value problems by finite elements.Apl. Mat. 33 (1988), 213-244. MR 0944785
Reference: [4] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction.Elsevier, Amsterdam 1981. MR 0600655
Reference: [5] I. Hlaváček J. Nečas: On inequalities of Korn's type.Arch. Rational Mech. Anal. 36 (1970), 305-334. MR 0252844, 10.1007/BF00249518
Reference: [6] J. A. Nitsche: On Korn's second inequality.R.A.I.R.O. Anal. numér., 15 (1981), 237-248. Zbl 0467.35019, MR 0631678, 10.1051/m2an/1981150302371
Reference: [7] T. Tiihonen: On Korn's inequality and shape optimization.Preprint 61, Univ. of Jyväskylä, Dept. of Math., April 1987. MR 0893392


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