The eigenvalue problem for the regional fractional Laplacian in the small order limit

2021/12/16 by Remi Yvant Temgoua, Temgoua, Remi Yvant, Tobias Weth +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2112.08856

openalex publication_date 2021/12/16 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this note, we study the asymptotic behavior of eigenvalues and eigenfunctions of the regional fractional Laplacian (-Δ)^s as s → 0⁺. Our analysis leads to a study of the regional logarithmic Laplacian, which arises as a formal derivative of regional fractional Laplacians at s = 0.

Cited by

• Nonlocal Dirichlet problems involving the Logarithmic p-Laplacian
• Sharp embeddings and existence results for Logarithmic p-Laplacian equations with critical growth

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