Rate of Convergence for Eigenfunctions of Aharonov-Bohm Operators with a Moving Pole

Abatangelo, Laura; Felli, Veronica

doi:10.1007/978-3-319-64489-9_1

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Continuity With Respect To the Poles1

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Cited by 2 publications

(1 citation statement)

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“…Remark 4.9. More results on the Aharonov-Bohm eigenvalues as function of the poles can be found in [24,76,30,1,72,4,2,5,3,6]. We have only emphasized in this section on the results which have direct applications to the research of candidates for minimal partitions.…”

Section: Continuity With Respect To the Polesmentioning

confidence: 99%

Nodal domains, spectral minimal partitions, and their relation to Aharonov-Bohm operators

Bonnaillie‐Noël¹,

Helffer²,

Hoffmann‐Ostenhof³

2017

Preprint

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This survey is a short version of a chapter written by the first two authors in the book [66] (where more details and references are given) but we have decided here to emphasize more on the role of the Aharonov-Bohm operators which appear to be a useful tool coming from physics for understanding a problem motivated either by spectral geometry or dynamics of population. Similar questions appear also in Bose-Einstein theory. Finally some open problems which might be of interest are mentioned.

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Section: Continuity With Respect To the Polesmentioning

confidence: 99%

Nodal domains, spectral minimal partitions, and their relation to Aharonov-Bohm operators

Bonnaillie‐Noël¹,

Helffer²,

Hoffmann‐Ostenhof³

2017

Preprint

View full text Add to dashboard Cite

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Estimates for eigenvalues of Aharonov–Bohm operators with varying poles and non-half-integer circulation

Abatangelo¹,

Felli²,

Noris³

et al. 2018

Analysis & PDE

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We study the behavior of eigenvalues of a magnetic Aharonov-Bohm operator with non-half-integer circulation and Dirichlet boundary conditions in a planar domain. As the pole is moving in the interior of the domain, we estimate the rate of the eigenvalue variation in terms of the vanishing order of the limit eigenfunction at the limit pole. We also provide an accurate blow-up analysis for scaled eigenfunctions and prove a sharp estimate for their rate of convergence.

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Rate of Convergence for Eigenfunctions of Aharonov-Bohm Operators with a Moving Pole

Abstract: We study the behavior of eigenfunctions for magnetic Aharonov-Bohm operators with halfinteger circulation and Dirichlet boundary conditions in a planar domain. We prove a sharp estimate for the rate of convergence of eigenfunctions as the pole moves in the interior of the domain.

Cited by 2 publications

References 15 publications

Nodal domains, spectral minimal partitions, and their relation to Aharonov-Bohm operators

Nodal domains, spectral minimal partitions, and their relation to Aharonov-Bohm operators

Estimates for eigenvalues of Aharonov–Bohm operators with varying poles and non-half-integer circulation

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