Dorin Bucur & Nicolas Varchon
Abstract:
We consider an elliptic operator, in divergence form, that is a
uniformly elliptic matrix. We describe the behavior of every sequence
of domains which minimizes the first Dirichlet eigenvalue over a
family of fixed measure domains of
.
The existence of minimizers is proved in some particular situations,
for example when the operator is periodic.
Submitted February 1-st, 2000. Published May 16, 2000.
Math Subject Classifications: 49Q10, 49R50.
Key Words: First eigenvalue, Dirichlet boundary, non-constant coeffcients,
optimal domain.
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Dorin Bucur Equipe de Mathematiques, UMR CNRS 6623 Universite; de Franche-Comte 16, route de Gray, 25030 Besancon Cedex, France email: bucur@math.univ-fcomte.fr |
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Nicolas Varchon Equipe de Mathematiques, UMR CNRS 6623 Universite; de Franche-Comte 16, route de Gray, 25030 Besancon Cedex, France email: varchon@math.univ-fcomte.fr |
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