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Effective operator for Robin eigenvalues in domains with corners

Khalile, Magda; Ourmières-Bonafos, Thomas; Pankrashkin, Konstantin (2018), Effective operator for Robin eigenvalues in domains with corners. https://basepub.dauphine.fr/handle/123456789/18686

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Type
Document de travail / Working paper
Date
2018
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
57
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Author(s)
Khalile, Magda
Laboratoire de Mathématiques d'Orsay [LMO]
Ourmières-Bonafos, Thomas
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Pankrashkin, Konstantin
Laboratoire de Mathématiques d'Orsay [LM-Orsay]
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."
Subjects / Keywords
Eigenvalue; Laplacian; Robin boundary condition; effective operator; non-smooth domain