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Strict convexity, strong ellipticity, and regularity in the calculus of variations

Published online by Cambridge University Press:  24 October 2008

J. M. Ball
J. M. Ball
Affiliation:
University of California, Berkeley
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Extract

In this paper we investigate the connection between strong ellipticity and the regularity of weak solutions to the equations of nonlinear elastostatics and other nonlinear systems arising from the calculus of variations. The main mathematical tool is a new characterization of continuously differentiable strictly convex functions. We first describe this characterization, and then explain how it can be applied to the calculus of variations and to elastostatics.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 3 , May 1980 , pp. 501 - 513
Copyright
Copyright © Cambridge Philosophical Society 1980

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