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A limiting solution for an ill-posed membrane problem

Published online by Cambridge University Press:  14 November 2011

A. A. Lacey
A. A. Lacey
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland
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Synopsis

We consider a perturbed version of a membrane problem when the latter has no solution. The modified problem has a solution which depends on a parameter ε > 0. As ε →0 this solution is seen to tend towards a “generalised solution” of the original problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 3-4 , 1986 , pp. 305 - 313
Copyright
Copyright © Royal Society of Edinburgh 1986

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References

1Ekeland, I. and Témam, R.. Analyse convexe et problèmes variationnels (Paris: Dunod, Gauthier-Villar, 1974).Google Scholar