Korn's inequalities: The linear vs. the nonlinear case

Philippe Ciarlet

doi:10.3934/dcdss.2012.5.473

Article Contents

2012, Volume 5, Issue 3: 473-483. Doi: 10.3934/dcdss.2012.5.473

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Korn's inequalities: The linear vs. the nonlinear case

Philippe Ciarlet^1,

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

Received: August 31, 2010

Published: May 2012

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Abstract

It is well known that the linear Korn inequality pervades the theory of three-dimensional linearized elasticity. It is thus conceivable that nonlinear Korn's inequalities could likewise play a role in the theory of three-dimensional nonlinear elasticity. In this paper, we describe the (available to this date) linear and nonlinear Korn's inequalities and we discuss the resemblances, but also the sometimes intriguing differences, that exist between these two kinds of inequalities.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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