Existence of minimizers for spectral problems

By Dario Mazzoleni, Aldo Pratelli. 2011

91 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f1a2baea8c73976556a43c738a35a00101e4ce4a

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In Applied Mathematics

1. Dorin Bucur
2. Antoine Henrot

In Computational Theory and Mathematics

1. Dorin Bucur
2. Antoine Henrot

In Mathematical Physics

1. Dorin Bucur
2. Antoine Henrot

Citations in the corpus

• Minimization of the k-th eigenvalue of the Dirichlet Laplacian (2012, background): “This argument, combined with the result of Buttazzo-Dal Maso, leads to the existence of (bounded) solutions for a general class of monotonous functionals of eigenvalues, so that the existence part of the result in Theorem 3 could also be obtained using [13].”