Inequalities of Korn's type, uniform with respect to a class of domains

Ivan Hlaváček

Aplikace matematiky (1989)

  • Volume: 34, Issue: 2, page 105-112
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Hlaváček, Ivan. "Inequalities of Korn's type, uniform with respect to a class of domains." Aplikace matematiky 34.2 (1989): 105-112. <http://eudml.org/doc/15568>.

@article{Hlaváček1989,
abstract = {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.},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {domain optimization; Korn’s inequality; Friedrichs inequality; domain optimization; Korn's inequality; Friedrichs inequality},
language = {eng},
number = {2},
pages = {105-112},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Inequalities of Korn's type, uniform with respect to a class of domains},
url = {http://eudml.org/doc/15568},
volume = {34},
year = {1989},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Inequalities of Korn's type, uniform with respect to a class of domains
JO - Aplikace matematiky
PY - 1989
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 2
SP - 105
EP - 112
AB - 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.
LA - eng
KW - domain optimization; Korn’s inequality; Friedrichs inequality; domain optimization; Korn's inequality; Friedrichs inequality
UR - http://eudml.org/doc/15568
ER -

References

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  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. (1986) MR0836802
  2. J. Nečas I. Hlaváček, Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, Elsevier, Amsterdam, 1981. (1981) MR0600655
  3. I. Hlaváček J. Nečas, 10.1007/BF00249518, Arch. Ratl. Mech. Anal. 36 (1970), 305-334. (1970) MR0252844DOI10.1007/BF00249518
  4. J. A. Nitsche, On Korn's second inequality, R.A.I.R.O. Anal. numer., 15 (1981), 237-248. (1981) Zbl0467.35019MR0631678
  5. T. Tiihonen, On Korn's inequality and shape optimization, Preprint No. 61, University of Jyväskylä, April 1987. (1987) MR0893392

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