Fractional Laplacian in V‐shaped waveguide

Fedor Bakharev and Sergey Matveenko

Mathematische Nachrichten, 2025, vol. 298, issue 2, 427-436

Abstract: The spectral properties of the restricted fractional Dirichlet Laplacian in V‐shaped waveguides are studied. The continuous spectrum for such domains with cylindrical outlets is known to occupy the ray [Λ†,+∞)$[\Lambda _\dagger, +\infty)$ with the threshold corresponding to the smallest eigenvalue of the cross‐sectional problems. In this work, the presence of a discrete spectrum at any junction angle is established along with the monotonic dependence of the discrete spectrum on the angle.

Date: 2025
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https://doi.org/10.1002/mana.202400271

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