Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 36, pp. 1-10.
Title: Global minimizing domains for the first eigenvalue of an elliptic
operator with non-constant coefficients
Authors: Dorin Bucur (Univ. de Franche-Comte, France)
Nicolas Varchon (Univ. de Franche-Comte, France)
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 $R^N$.
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.