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- W2974162596 abstract "Let Γ⊂R2 be a simple closed curve which is smooth except at the origin, at which it has a power cusp and coincides with the curve |x2|=x1p for some p>1. We study the eigenvalues of the Schrödinger operator Hα with the attractive δ-potential of strength α>0 supported by Γ, which is defined by its quadratic formH1(R2)∋u↦∬R2|∇u|2dx−α∫Γu2ds, where ds stands for the one-dimensional Hausdorff measure on Γ. It is shown that if n∈N is fixed and α is large, then the well-defined nth eigenvalue En(Hα) of Hα behaves asEn(Hα)=−α2+22p+2Enα6p+2+O(α6p+2−η), where the constants En>0 are the eigenvalues of an explicitly given one-dimensional Schrödinger operator determined by the cusp, and η>0. Both main and secondary terms in this asymptotic expansion are different from what was observed previously for the cases when Γ is smooth or piecewise smooth with non-zero angles." @default.
- W2974162596 created "2019-09-26" @default.
- W2974162596 creator A5046730581 @default.
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- W2974162596 date "2020-11-01" @default.
- W2974162596 modified "2023-09-25" @default.
- W2974162596 title "Strong coupling asymptotics for δ-interactions supported by curves with cusps" @default.
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- W2974162596 doi "https://doi.org/10.1016/j.jmaa.2020.124287" @default.
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