In this paper we prove that the shape optimization problem {λk (Ω) : Ω ⊂ ℝd, Ω open, P(Ω) = 1, |Ω| <+ ∞- has a solution for any k ∈ ℕ and dimension d. Moreover, every solution is a bounded connected open set with boundary which is C 1,α outside a closed set of Hausdorff dimension d-8. Our results are more general and apply to spectral functionals of the form λk1 (Ω)⋯ λkp (Ω)), for increasing functions f satisfying some suitable bi-Lipschitz type condition. © 2013 Springer Science+Business Media New York.

Existence and Regularity of Minimizers for Some Spectral Functionals with Perimeter Constraint

De Philippis, Guido;
2014-01-01

Abstract

In this paper we prove that the shape optimization problem {λk (Ω) : Ω ⊂ ℝd, Ω open, P(Ω) = 1, |Ω| <+ ∞- has a solution for any k ∈ ℕ and dimension d. Moreover, every solution is a bounded connected open set with boundary which is C 1,α outside a closed set of Hausdorff dimension d-8. Our results are more general and apply to spectral functionals of the form λk1 (Ω)⋯ λkp (Ω)), for increasing functions f satisfying some suitable bi-Lipschitz type condition. © 2013 Springer Science+Business Media New York.
2014
69
2
199
231
https://arxiv.org/abs/1303.0968
http://cdsads.u-strasbg.fr/abs/2013arXiv1303.0968D
De Philippis, Guido; Velichkov, B.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/14562
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