Global minimizing domains for the first eigenvalue of an elliptic operator with non-constant coefficients
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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 ℝN. The existence of minimizers is proved in some particular situations, for example when the operator is periodic.
CitationBucur, D., & Varchon, N. (2000). Global minimizing domains for the first eigenvalue of an elliptic operator with non-constant coefficients. Electronic Journal of Differential Equations, 2000(36), pp. 1-10.
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