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

Germán Miranda

doi:10.1007/s00013-023-01848-z

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

Germán Miranda

Matematik LTH

Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

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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 + ∞.

Originalspråk	engelska
Sidor (från-till)	643-649
Antal sidor	7
Tidskrift	Archiv der Mathematik
Volym	120
Nummer	6
DOI	https://doi.org/10.1007/s00013-023-01848-z
Status	Published - 2023 juni

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Matematisk analys

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10.1007/s00013-023-01848-zLicens: CC BY

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title = "Non-monotonicity of the first eigenvalue for the 3D magnetic Robin Laplacian",

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 + ∞.",

keywords = "Magnetic Robin Laplacian, Non-monotonicity, Perturbation theory",

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AB - 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 + ∞.

KW - Magnetic Robin Laplacian

KW - Non-monotonicity

KW - Perturbation theory

U2 - 10.1007/s00013-023-01848-z

DO - 10.1007/s00013-023-01848-z

M3 - Article

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

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