Existence of discrete eigenvalues for the Dirichlet Laplacian in a two-dimensional twisted strip

2020/09/30 by Rafael T. Amorim, Amorim, Rafael T., Alessandra A. Verri +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2010.00034

openalex publication_date 2020/09/30 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28

Abstract

We study the spectrum of the Dirichlet Laplacian operator in a two-dimensional twisted strip embedded in \mathbb R^d with d ≥ 2. It is shown that a local twisting perturbation can create discrete eigenvalues for the operator. In particular, we also study the case where the twisted effect "grows" at infinity while the width of the strip goes to zero. In this situation, we find an asymptotic behavior for the eigenvalues.

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