Opuscula Mathematica
Opuscula Math. 45, no. 3 (2025), 293-305

Magnetic Dirichlet Laplacian in curved waveguides

Diana Barseghyan
Swanhild Bernstein
Baruch Schneider
Martha Lina Zimmermann
Abstract. For a two-dimensional curved waveguide, it is well known that the spectrum of the Dirichlet Laplacian is unstable with respect to waveguide deformations. This means that if the waveguide is a straight strip then the spectrum of the Dirichlet Laplacian is purely essential. From the other hand, the perturbation of the straight strip produces eigenvalues below the essential spectrum. In this paper, the Dirichlet-Laplace operator with a magnetic field is considered. We explicitly prove that the spectrum of the magnetic Laplacian is stable under small but non-local deformations of the waveguide.
Keywords: magnetic Schrödinger operators, essential spectrum, discrete spectrum.
Mathematics Subject Classification: 35P15, 81Q10.
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About the authors ▼
Diana Barseghyan (corresponding author)
https://orcid.org/0000-0003-0761-1157
University of Ostrava, Department of Mathematics, 30. dubna 22, 70103 Ostrava, Czech Republic
Swanhild Bernstein
https://orcid.org/0000-0002-8603-6682
Technische Universität Bergakademie Freiberg, Institute of Applied Analysis, Akademiestrasse 6, Freiberg 09599, Germany
Baruch Schneider
https://orcid.org/0000-0003-2933-3899
University of Ostrava, Department of Mathematics, 30. dubna 22, 70103 Ostrava, Czech Republic
Martha Lina Zimmermann
https://orcid.org/0000-0003-0030-1025
Technische Universität Bergakademie Freiberg, Institute of Applied Analysis, Akademiestrasse 6, Freiberg 09599, Germany
About the article ▼
Communicated by P.A. Cojuhari.
Received: 2025-04-15.
Revised: 2025-04-21.
Accepted: 2025-04-23.
Published online: 2025-05-30.
Cite this article as ▼
Diana Barseghyan, Swanhild Bernstein, Baruch Schneider, Martha Lina Zimmermann, Magnetic Dirichlet Laplacian in curved waveguides, Opuscula Math. 45, no. 3 (2025), 293-305, https://doi.org/10.7494/OpMath.2025.45.3.293.
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