PreprintCC BY-NC-ND 4.0arXiv
Spectral properties of the magnetic Robin Laplacian on curvilinear half-plane
Abstract
We analyse magnetic Robin Laplacian in curvilinear half-plane with a smooth boundary. It is well known that the spectrum of the Robin Laplacian is unstable with respect to boundary deformations. This means that if the boundary is a straight line then the spectrum of the Robin Laplacian is purely essential. From the other hand, the perturbation of the boundary produces eigenvalues below the essential spectrum. In this paper, the Robin-Laplace operator with a compactly supported magnetic field is considered. We prove that the spectrum of the magnetic Robin Laplacian is stable under small and local deformations of the boundary.
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BibTeX
@misc{barseghyan2026spectral,
title = {{Spectral properties of the magnetic Robin Laplacian on curvilinear half-plane}},
author = {Diana Barseghyan and Baruch Schneider and Yifan Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03783},
eprint = {2609.03783},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03783},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Spectral properties of the magnetic Robin Laplacian on curvilinear half-plane
AU - Diana Barseghyan
AU - Baruch Schneider
AU - Yifan Zhang
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03783
UR - https://arxiv.org/abs/2609.03783
AB - We analyse magnetic Robin Laplacian in curvilinear half-plane with a smooth boundary. It is well known that the spectrum of the Robin Laplacian is unstable with respect to boundary deformations. This means that if the boundary is a straight line then the spectrum of the Robin Laplacian is purely essential. From the other hand, the perturbation of the boundary produces eigenvalues below the essential spectrum. In this paper, the Robin-Laplace operator with a compactly supported magnetic field is considered. We prove that the spectrum of the magnetic Robin Laplacian is stable under small and local deformations of the boundary.
ER -