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.

Existence of minimizers for spectral problems

MAZZOLENI, DARIO CESARE SEVERO;PRATELLI, ALDO
2013-01-01

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/894238
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