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- W4301477860 abstract "Let $Omega$ be a curvilinear polygon and $Q^gamma_{Omega}$ be the Laplacian in $L^2(Omega)$, $Q^gamma_{Omega}psi=-Delta psi$, with the Robin boundary condition $partial_nu psi=gamma psi$, where $partial_nu$ is the outer normal derivative and $gamma>0$. We are interested in the behavior of the eigenvalues of $Q^gamma_Omega$ as $gamma$ becomes large. We prove that the asymptotics of the first eigenvalues of $Q^gamma_Omega$ is determined at the leading order by those of model operators associated with the vertices: the Robin Laplacians acting on the tangent sectors associated with $partial Omega$. In the particular case of a polygon with straight edges the first eigenpairs are exponentially close to those of the model operators. Finally, we prove a Weyl asymptotics for the eigenvalue counting function of $Q^gamma_Omega$ for a threshold depending on $gamma$, and show that the leading term is the same as for smooth domains." @default.
- W4301477860 created "2022-10-05" @default.
- W4301477860 creator A5002504753 @default.
- W4301477860 date "2017-10-26" @default.
- W4301477860 modified "2023-09-27" @default.
- W4301477860 title "Spectral asymptotics for Robin Laplacians on polygonal domains" @default.
- W4301477860 doi "https://doi.org/10.48550/arxiv.1710.09679" @default.
- W4301477860 hasPublicationYear "2017" @default.
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