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June 2012, 5(3): 473-483. doi: 10.3934/dcdss.2012.5.473
Korn's inequalities: The linear vs. the nonlinear case
Philippe Ciarlet 1,
City University of Hong Kong, Department of Mathematics, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, China
Received September 2010 Published October 2011
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.
Keywords: multifractal analysis., Poincaré recurrences, Dimension theory.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Philippe Ciarlet. Korn's inequalities: The linear vs. the nonlinear case. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 473-483. doi: 10.3934/dcdss.2012.5.473
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Philippe Ciarlet