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On Korn’s inequality

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Abstract

The author first reviews the classical Korn inequality and its proof. Following recent works of S. Kesavan, P. Ciarlet, Jr., and the author, it is shown how the Korn inequality can be recovered by an entirely different proof. This new proof hinges on appropriate weak versions of the classical Poincaré and Saint-Venant lemma. In fine, both proofs essentially depend on a crucial lemma of J. L. Lions, recalled at the beginning of this paper.

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Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China

    Philippe G. Ciarlet

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  1. Philippe G. Ciarlet
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Correspondence to Philippe G. Ciarlet.

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Dedicated to Professor Roger Temam on the Occasion of his 70th Birthday

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Ciarlet, P.G. On Korn’s inequality. Chin. Ann. Math. Ser. B 31, 607–618 (2010). https://doi.org/10.1007/s11401-010-0606-3

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  • DOI: https://doi.org/10.1007/s11401-010-0606-3

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