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Title: Inequalities of Korn's type, uniform with respect to a class of domains (English)
Author: Hlaváček, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 34
Issue: 2
Year: 1989
Pages: 105-112
Summary lang: English
Category: math
Summary: Inequalities of Korn's type involve a positive constant, which depends on the domain, in general. A question arises, whether the constants possess a positive infimum, if a class of bounded two-dimensional domains with Lipschitz boundary is considered. The proof of a positive answer to this question is shown for several types of boundary conditions and for two classes of domains. (English)
Keyword: domain optimization
Keyword: Korn’s inequality
Keyword: Friedrichs inequality
MSC: 35J20
MSC: 35J55
MSC: 49A22
MSC: 49J20
idZBL: Zbl 0673.49003
idMR: MR0990298
DOI: 10.21136/AM.1989.104339
Date available: 2008-05-20T18:36:12Z
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] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction.Elsevier, Amsterdam, 1981. MR 0600655
Reference: [3] I. Hlaváček J. Nečas: On inequalities of Korn's type.Arch. Ratl. Mech. Anal. 36 (1970), 305-334. MR 0252844, 10.1007/BF00249518
Reference: [4] J. A. Nitsche: On Korn's second inequality.R.A.I.R.O. Anal. numer., 15 (1981), 237-248. Zbl 0467.35019, MR 0631678
Reference: [5] T. Tiihonen: On Korn's inequality and shape optimization.Preprint No. 61, University of Jyväskylä, April 1987. MR 0893392


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