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

Aplikace matematiky (1989)

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

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topHlaváček, 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

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

## Citations in EuDML Documents

top- Jaroslav Haslinger, Raino Mäkinen, Shape optimization of materially non-linear bodies in contact
- Ivan Hlaváček, Michal Křížek, Weight minimization of elastic bodies weakly supporting tension. II. Domains with two curved sides
- Ivan Hlaváček, Korn's inequality uniform with respect to a class of axisymmetric bodies
- Ivan Hlaváček, Michal Křížek, Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side

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