Previous |  Up |  Next


domain optimization; shape optimization; Korn’s inequality
The Korn's inequality involves a positive constant, which depends on the domains, in general. We prove that the constants have a positive infimum, if a class of bounded axisymmetric domains and axisymmetric displacement fields are considered.
[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
[2] I. Hlaváček: Inequalities of Korn's type, uniform with respect to a class of domains. Apl. Mat. Zbl 0673.49003
[3] I. Hlaváček: Domain optimization in axisymmetric elliptic boundary value problems by finite elements. Apl. Mat. 33 (1988), 213-244. MR 0944785
[4] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Elsevier, Amsterdam 1981. MR 0600655
[5] I. Hlaváček J. Nečas: On inequalities of Korn's type. Arch. Rational Mech. Anal. 36 (1970), 305-334. DOI 10.1007/BF00249518 | MR 0252844
[6] J. A. Nitsche: On Korn's second inequality. R.A.I.R.O. Anal. numér., 15 (1981), 237-248. MR 0631678 | Zbl 0467.35019
[7] T. Tiihonen: On Korn's inequality and shape optimization. Preprint 61, Univ. of Jyväskylä, Dept. of Math., April 1987. MR 0893392
Partner of
EuDML logo