Geodesic
Global minimizing domains for the first eigenvalue of an elliptic operator with non-constant coefficients
Electronic journal of differential equations, Tome 2000 (2000)
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__a33,
     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},
     year = {2000},
     volume = {2000},
     zbl = {0958.49024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a33/}
}
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%A Varchon,  Nicolas
%T Global minimizing domains for the first eigenvalue of an elliptic operator with non-constant coefficients
%J Electronic journal of differential equations
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%V 2000
%U http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a33/
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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__a33/