Fractional Laplacian in bended strip

2025/11/24 by Bakharev, Fedor, Matveenko, Sergey
Mathematics · #35R11 #81Q10 #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.2511.19296

openalex publication_date 2025/11/24 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28

Abstract

The spectral properties of the restricted fractional Laplacian with Dirichlet boundary conditions in a smoothly bent waveguide is investigated. The existence of eigenvalues below the threshold of the continuous spectrum is proved, generalizing classical results known for the local Laplace operator. Our approach utilizes the Caffarelli--Silvestre extension, addressing the specific geometric difficulties arising from the operator non-locality. The sufficient conditions on the curvature magnitude and distribution to ensure the existence of these trapped modes is established.

Citations

• Fractional Laplacian in V-shaped waveguide
• Dirichlet Fractional Laplacian in multi-tubes
• From the long jump random walk to the fractional Laplacian

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