Extended Korn's inequalities and the associated best possible constants |
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Authors: | Hiroya Ito |
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Institution: | (1) Department of Mathematics, Tokyo Institute of Technology, 152 Tokyo, Japan;(2) Present address: Department of Mathematics, Shinshu University, 390 Matsumato, Japan |
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Abstract: | We are concerned with the coerciveness of the strain energy E(u) (in linear elasticity) associated with a displacement vector u on the Sobolev space H1 () or its subspaces, a domain in n representing an isotropic elastic body—certain specific cases are called Korn's inequalities. Sufficient (and necessary) conditions on the Lamé moduli for E(·) to be coercive (or uniformly positive) on such spaces are given, and the associated best possible constants are obtained for some cases. |
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Keywords: | 35B45 73C99 |
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