A note on contact shape optimization with semicoercive state problems

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. © 2002 Mathematical Institute, Academy of Sciences of Czech Republic.