Fractional Laplacian in V-shaped waveguide

2024/05/27 by F. L. Bakharev, Bakharev, Fedor, S. I. Matveenko +1 · 2 citations
Engineering · Physics and Astronomy · #35R11 #81Q10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Engineering and Waveguides #Photonic Crystals and Applications #Photonic and Optical Devices #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2405.16892

openalex publication_date 2024/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The spectral properties of the restricted fractional Dirichlet Laplacian in \sf V-shaped waveguides are studied. The continuous spectrum for such domains with cylindrical outlets is known to occupy the ray [Λ_†, +∞) 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.

Cited by

• Fractional Laplacian in bended strip
• Monotonicity of discrete spectra of Dirichlet Laplacian in 3-dimensional layers

Related

• Fractional Laplacian in bended strip
• Spectrum of the Dirichlet Laplacian in waveguides with parallel cross-sections
• Spectrum of the Laplacian in waveguide shaped surfaces
• Dirichlet Fractional Laplacian in multi-tubes
• A note on the spectrum of the Neumann Laplacian in periodic waveguides