Korn’s inequality uniform with respect to a class of axisymmetric bodies. (English) Zbl 0673.49004

Summary: The Korn’s inequality involves a positive constant, which depends on the domain, in general. We prove that the constants have a positive infimum, if a class of bounded axisymmetric domains and axisymmetric displacement fields are considered.


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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