Inequalities of Korn’s type, uniform with respect to a class of domains. (English) Zbl 0673.49003

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.


49J20 Existence theories for optimal control problems involving partial differential equations
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
74B99 Elastic materials
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