Hlaváček, Ivan Inequalities of Korn’s type, uniform with respect to a class of domains. (English) Zbl 0673.49003 Apl. Mat. 34, No. 2, 105-112 (1989). Summary: Inequalities of Korn’s type involve a positive constant, which depends on the domain, in general. The 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 the positive answer to this question is shown for several types of boundary conditions and for two classes of domains. Cited in 8 Documents MSC: 49J20 Existence theories for optimal control problems involving partial differential equations 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 74B99 Elastic materials Keywords:domain optimization; Korn’s inequality; Friedrichs inequality PDF BibTeX XML Cite \textit{I. Hlaváček}, Apl. Mat. 34, No. 2, 105--112 (1989; Zbl 0673.49003) Full Text: EuDML References: [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. · Zbl 0594.73109 [2] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Elsevier, Amsterdam, 1981. [3] I. Hlaváček J. Nečas: On inequalities of Korn’s type. Arch. Ratl. Mech. Anal. 36 (1970), 305-334. · Zbl 0193.39001 [4] J. A. Nitsche: On Korn’s second inequality. R.A.I.R.O. Anal. numer., 15 (1981), 237-248. · Zbl 0467.35019 [5] T. Tiihonen: On Korn’s inequality and shape optimization. Preprint No. 61, University of Jyväskylä, April 1987. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.