In this paper we show that any increasing functional of the first k eigenvalues of the Dirichlet Laplacian admits a (quasi-)open minimizer among the subsets of R^N of unit measure. In particular, there exists such a minimizer which is bounded, where the bound depends on k and N, but not on the functional.
Mazzoleni, D. C. S., Pratelli, A., Existence of minimizers for spectral problems, <<JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES>>, 2013; 100 (3): 433-453. [doi:10.1016/j.matpur.2013.01.008] [http://hdl.handle.net/10807/118947]
Existence of minimizers for spectral problems
Mazzoleni, Dario Cesare Severo;
2013
Abstract
In this paper we show that any increasing functional of the first k eigenvalues of the Dirichlet Laplacian admits a (quasi-)open minimizer among the subsets of R^N of unit measure. In particular, there exists such a minimizer which is bounded, where the bound depends on k and N, but not on the functional.
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