Geodesic
A note on contact shape optimization with semicoercive state problems
Applications of Mathematics, Tome 47 (2002) no. 5, pp. 397-410.

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This note deals with contact shape optimization for problems involving “floating” structures. The boundedness of solutions to state problems with respect to admissible domains, which is the basic step in the existence analysis, is a consequence of Korn’s inequality in coercive cases. In semicoercive cases (meaning that floating bodies are admitted), the Korn inequality cannot be directly applied and one has to proceed in another way: to use a decomposition of kinematically admissible functions and a Korn type inequality on appropriate subspaces. In addition, one has to show that the constant appearing in this inequality is independent with respect to a family of admissible domains.
DOI : 10.1023/A:1021709907750
Classification : 49A29, 65K10, 73K25
Mots-clés : shape optimization; semicoercive problems 
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Haslinger, Jaroslav. A note on contact shape optimization with semicoercive state problems. Applications of Mathematics, Tome 47 (2002) no. 5, pp. 397-410. doi : 10.1023/A:1021709907750. https://geodesic-test.mathdoc.fr/articles/10.1023/A:1021709907750/

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