Geodesic
Global minimizing domains for the first eigenvalue of an elliptic operator with non-constant coefficients
Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 49Q10, 49R50
Keywords: first eigenvalue, Dirichlet boundary, non-constant coeffcients, optimal domain 
@article{EJDE_2000__2000__a179,
     author = {Bucur, Dorin and Varchon, Nicolas},
     title = {Global minimizing domains for the first eigenvalue of an elliptic operator with non-constant coefficients},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a179/}
}
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Bucur, Dorin; Varchon, Nicolas. Global minimizing domains for the first eigenvalue of an elliptic operator with non-constant coefficients. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a179/