Article
Keywords:
domain optimization; shape optimization; Korn’s inequality
Summary:
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.
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.
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
[7] T. Tiihonen:
On Korn's inequality and shape optimization. Preprint 61, Univ. of Jyväskylä, Dept. of Math., April 1987.
MR 0893392