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Shape optimisation problems governed by nonlinear state equations

Published online by Cambridge University Press:  14 November 2011

Dorin Bucur  and
Paola Trebeschi
Dorin Bucur
Affiliation:
CNRS-Equipe de Mathématiques, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France, e-mail: [email protected]
Paola Trebeschi
Affiliation:
Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy, e-mail: [email protected]
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Abstract

The purpose of this paper is to give a compactness-continuity result for the solution of a nonlinear Dirichlet problem in terms of its domain variation. The topology in the family of domains is given by the Hausdorff metric and continuity is obtained under capacity conditions. A generalisation of Sverak's result in iV-dimensions is deduced as a particular case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 5 , 1998 , pp. 945 - 963
Copyright
Copyright © Royal Society of Edinburgh 1998

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