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Article Dans Une Revue Annales de l'Institut Fourier Année : 2021

Effective operator for Robin eigenvalues in domains with corners

Résumé

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.

Dates et versions

hal-01947690 , version 1 (07-12-2018)

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Magda Khalile, Thomas Ourmières-Bonafos, Konstantin Pankrashkin. Effective operator for Robin eigenvalues in domains with corners. Annales de l'Institut Fourier, 2021, ⟨10.5802/aif.3400⟩. ⟨hal-01947690⟩
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