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The displacement problem for elastic crystals

Published online by Cambridge University Press:  14 November 2011

I. Fonseca  and
L. Tartar
I. Fonseca
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
L. Tartar
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
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Synopsis

In this paper we obtain necessary and sufficient conditions for the existence of Lipschitz minimisers of a functional of the type

where h is a convex function converging to infinity at zero and u is subjected to displacement boundary conditions. We provide examples of body forces f for which the infimum of J(.) is not attained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 113 , Issue 1-2 , 1989 , pp. 159 - 180
Copyright
Copyright © Royal Society of Edinburgh 1989

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