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Non-monotonicity of the first eigenvalue for the 3D magnetic Robin Laplacian

Miranda, Germán LU (2023) In Archiv der Mathematik 120(6). p.643-649
Abstract

Previous works provided several counterexamples to monotonicity of the lowest eigenvalue for the magnetic Laplacian in the two-dimensional case. However, the three-dimensional case is less studied. We use the results obtained by Helffer, Kachmar, and Raymond to provide one of the first counterexamples in 3D. Considering the magnetic Robin Laplacian on the unit ball with a constant magnetic field, we show the non-monotonicity of the lowest eigenvalue asymptotics when the Robin parameter tends to + ∞.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Magnetic Robin Laplacian, Non-monotonicity, Perturbation theory
in
Archiv der Mathematik
volume
120
issue
6
pages
7 pages
publisher
Birkhäuser Verlag
external identifiers
  • scopus:85150224079
ISSN
0003-889X
DOI
10.1007/s00013-023-01848-z
language
English
LU publication?
yes
id
64271050-cf97-4ed1-a2e2-183989057e62
date added to LUP
2023-07-05 13:08:27
date last changed
2023-07-05 13:08:27
@article{64271050-cf97-4ed1-a2e2-183989057e62,
  abstract     = {{<p>Previous works provided several counterexamples to monotonicity of the lowest eigenvalue for the magnetic Laplacian in the two-dimensional case. However, the three-dimensional case is less studied. We use the results obtained by Helffer, Kachmar, and Raymond to provide one of the first counterexamples in 3D. Considering the magnetic Robin Laplacian on the unit ball with a constant magnetic field, we show the non-monotonicity of the lowest eigenvalue asymptotics when the Robin parameter tends to + ∞.</p>}},
  author       = {{Miranda, Germán}},
  issn         = {{0003-889X}},
  keywords     = {{Magnetic Robin Laplacian; Non-monotonicity; Perturbation theory}},
  language     = {{eng}},
  number       = {{6}},
  pages        = {{643--649}},
  publisher    = {{Birkhäuser Verlag}},
  series       = {{Archiv der Mathematik}},
  title        = {{Non-monotonicity of the first eigenvalue for the 3D magnetic Robin Laplacian}},
  url          = {{http://dx.doi.org/10.1007/s00013-023-01848-z}},
  doi          = {{10.1007/s00013-023-01848-z}},
  volume       = {{120}},
  year         = {{2023}},
}