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An example of H1-unboundedness of solutions to strongly elliptic systems of partial differential equations in a laminated geometry

Published online by Cambridge University Press:  14 November 2011

Hervé Le Dret
Hervé Le Dret
Affiliation:
Laboratoire d'Analyse Numérique, Tour 55-65, 5è étage, Université P.& M. Curie, 75252 Paris Cedex 05, France
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Synopsis

In this paper, a counterexample is given to the H1-boundedness of solutions to a sequence of systems of linear partial differential equations uniformly satisfying a strict Legendre–Hadamard condition and whose coefficients depend on one direction only. This counterexample is relevant for the theory of homogenisation of laminated elastic materials.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 77 - 82
Copyright
Copyright © Royal Society of Edinburgh 1987

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