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Keywords:
domain optimization; Korn’s inequality; Friedrichs inequality
domain optimization; Korn’s inequality; Friedrichs inequality
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.
References:
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[2] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Elsevier, Amsterdam, 1981. MR 0600655
[3] I. Hlaváček J. Nečas: On inequalities of Korn's type. Arch. Ratl. Mech. Anal. 36 (1970), 305-334. DOI 10.1007/BF00249518 | MR 0252844
[4] J. A. Nitsche: On Korn's second inequality. R.A.I.R.O. Anal. numer., 15 (1981), 237-248. MR 0631678 | Zbl 0467.35019
[5] T. Tiihonen: On Korn's inequality and shape optimization. Preprint No. 61, University of Jyväskylä, April 1987. MR 0893392
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