Opuscula Math. 45, no. 3 (2025), 293-305
https://doi.org/10.7494/OpMath.2025.45.3.293
Opuscula Mathematica
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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- 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
- Communicated by P.A. Cojuhari.
- Received: 2025-04-15.
- Revised: 2025-04-21.
- Accepted: 2025-04-23.
- Published online: 2025-05-30.
