In this paper we look for the domains minimizing the hth eigenvalue of the Dirichlet-Laplacian λh with a constraint on the diameter. Existence of an optimal domain is easily obtained and is attained at a constant width body. In the case of a simple eigenvalue, we provide nonstandard (i.e., nonlocal) optimality conditions. Then we address the question of whether the disk is an optimal domain in the plane, and we give the precise list of the 17 eigenvalues for which the disk is a local minimum. We conclude by some numerical simulations showing the 20 first optimal domains in the plane.

Minimization of the eigenvalues of the dirichlet-laplacian with a diameter constraint

Lucardesi I.
2018-01-01

Abstract

In this paper we look for the domains minimizing the hth eigenvalue of the Dirichlet-Laplacian λh with a constraint on the diameter. Existence of an optimal domain is easily obtained and is attained at a constant width body. In the case of a simple eigenvalue, we provide nonstandard (i.e., nonlocal) optimality conditions. Then we address the question of whether the disk is an optimal domain in the plane, and we give the precise list of the 17 eigenvalues for which the disk is a local minimum. We conclude by some numerical simulations showing the 20 first optimal domains in the plane.
2018
Bogosel, B.; Henrot, A.; Lucardesi, I.
File in questo prodotto:
File Dimensione Formato  
bogosel-et-al-2018-minimization-of-the-eigenvalues-of-the-dirichlet-laplacian-with-a-diameter-constraint.pdf

accesso aperto

Tipologia: Versione finale editoriale
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 543.49 kB
Formato Adobe PDF
543.49 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1210928
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? 9
social impact