Rendiconti del Seminario Matematico della Università di Padova

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Volume 135, 2016, pp. 207–221
DOI: 10.4171/RSMUP/135-12

Boundedness of minimizers for spectral problems in $\mathbb R^N$

Dario Mazzoleni[1]

(1) Dipartimento di Matematica, Università degli Studi di Torino, Via Carlo Alberto 10, 10123, Torino, Italy

In [8] it was proved that any increasing functional of the first $k$ eigenvalues of the Dirichlet Laplacian admits a (quasi-)open minimizer among the subsets of $\mathbb R^N$ of unit measure. In this paper we show that every minimizer is uniformly bounded by a constant depending only on $k,N$.

Keywords: Shape optimization, Dirichlet Laplacian, eigenvalues, spectral problems

Mazzoleni Dario: Boundedness of minimizers for spectral problems in $\mathbb R^N$. Rend. Sem. Mat. Univ. Padova 135 (2016), 207-221. doi: 10.4171/RSMUP/135-12