Boundedness of minimizers for spectral problems in ℝ N
Mazzoleni, Dario1
1 Università degli Studi di Torino, TORINO, ITALY
Rendiconti del Seminario Matematico della Università di Padova, Tome 135 (2016), pp. 207-221.

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

DOI : 10.4171/RSMUP/135-12
Classification : 49, 65
Mots-clés : Shape optimization, Dirichlet Laplacian, eigenvalues, spectral problems
Mazzoleni, Dario 1

1 Università degli Studi di Torino, TORINO, ITALY 
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     title = {Boundedness of minimizers for spectral problems in $\mathbb R^N$},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {207--221},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {135},
     year = {2016},
     doi = {10.4171/RSMUP/135-12},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/135-12/}
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Mazzoleni, Dario. Boundedness of minimizers for spectral problems in $\mathbb R^N$. Rendiconti del Seminario Matematico della Università di Padova, Tome 135 (2016), pp. 207-221. doi : 10.4171/RSMUP/135-12. http://www.numdam.org/articles/10.4171/RSMUP/135-12/

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