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Effective operators for Robin eigenvalues in domains with corners

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arxiv 1809.04998 v3 pith:4WX2AMA7 submitted 2018-09-13 math.SP math-phmath.APmath.MP

Magda Khalile , Thomas Ourmières-Bonafos , Konstantin Pankrashkin This is my paper · ORCID
classification math.SPmath-phmath.APmath.MP
keywords eigenvaluesboundaryasymptoticscornerseffectiveeigenvaluerobinassumptions
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons

    math.SP 2019-08 accept novelty 8.0 of 10

    Steklov eigenvalues of curvilinear polygons are asymptotically equal to explicit quasi-eigenvalues built from side lengths and angles, with errors tending to zero.

  2. On the eigenvalues of the Robin Laplacian with a complex parameter

    math.SP 2019-08 conditional novelty 8.0 of 10

    A dichotomy for complex Robin eigenvalues at large boundary parameter, with new numerical range bounds, a Dirichlet-to-Neumann proof, and interval, rectangle and ball asymptotics.

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