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Effective operator for Robin eigenvalues in domains with corners

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1809.04998.pdf (867.7Kb)
Date
2018
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Dewey
Sciences connexes (physique, astrophysique)
Sujet
Eigenvalue; Laplacian; Robin boundary condition; effective operator; non-smooth domain
URI
https://basepub.dauphine.fr/handle/123456789/18686
Collections
  • CEREMADE : Publications
Metadata
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Author
Khalile, Magda
245281 Laboratoire de Mathématiques d'Orsay [LMO]
Ourmières-Bonafos, Thomas
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Pankrashkin, Konstantin
40 Laboratoire de Mathématiques d'Orsay [LM-Orsay]
Type
Document de travail / Working paper
Item number of pages
57
Abstract (EN)
We study the eigenvalues of the Laplacian with a strong attractive Robin boundary condition in curvilinear polygons. It was known from previous works that the asymptotics of several first eigenvalues is essentially determined by the corner openings, while only rough estimates were available for the next eigenvalues. Under some geometric assumptions, we go beyond the critical eigenvalue number and give a precise asymptotics of any individual eigenvalue by establishing a link with an effective Schr\odinger-type operator on the boundary of the domain with boundary conditions at the corners."

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