Inequalities for the lowest magnetic Neumann eigenvalue

S. Fournais; B. Helffer

doi:10.1007/s11005-018-01154-8

Inequalities for the lowest magnetic Neumann eigenvalue

S. Fournais^*, B. Helffer

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

We study the ground-state energy of the Neumann magnetic Laplacian on planar domains. For a constant magnetic field, we consider the question whether the disc maximizes this eigenvalue for fixed area. More generally, we discuss old and new bounds obtained on this problem.

Original language	English
Journal	Letters in Mathematical Physics
Volume	109
Issue	7
Pages (from-to)	1683-1700
Number of pages	18
ISSN	0377-9017
DOIs	https://doi.org/10.1007/s11005-018-01154-8
Publication status	Published - Jul 2019

Keywords

Isoperimetric inequalities
Magnetic Faber-Krahn inequality
Spectral theory

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10.1007/s11005-018-01154-8

https://arxiv.org/pdf/1706.01950.pdf

Cite this

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title = "Inequalities for the lowest magnetic Neumann eigenvalue",

abstract = "We study the ground-state energy of the Neumann magnetic Laplacian on planar domains. For a constant magnetic field, we consider the question whether the disc maximizes this eigenvalue for fixed area. More generally, we discuss old and new bounds obtained on this problem.",

keywords = "Isoperimetric inequalities, Magnetic Faber-Krahn inequality, Spectral theory",

author = "S. Fournais and B. Helffer",

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AU - Fournais, S.

AU - Helffer, B.

PY - 2019/7

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AB - We study the ground-state energy of the Neumann magnetic Laplacian on planar domains. For a constant magnetic field, we consider the question whether the disc maximizes this eigenvalue for fixed area. More generally, we discuss old and new bounds obtained on this problem.

KW - Isoperimetric inequalities

KW - Magnetic Faber-Krahn inequality

KW - Spectral theory

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DO - 10.1007/s11005-018-01154-8

M3 - Journal article

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VL - 109

SP - 1683

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JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

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ER -

Inequalities for the lowest magnetic Neumann eigenvalue

Abstract

Keywords

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Semiclassical Quantum Mechanics

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Inequalities for the lowest magnetic Neumann eigenvalue

Abstract

Keywords

Access to Document

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Fingerprint

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Semiclassical Quantum Mechanics

Cite this