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Advanced Nonlinear Studies

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Volume 17, Issue 2


On Aharonov–Bohm Operators with Two Colliding Poles

Laura Abatangelo / Veronica Felli
  • Corresponding author
  • Dipartimento di Scienza dei Materiali, Università di Milano–Bicocca, Via Cozzi 55, 20125 Milano, Italy
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/ Corentin Léna
Published Online: 2017-03-18 | DOI: https://doi.org/10.1515/ans-2017-0004


We consider Aharonov–Bohm operators with two poles and prove sharp asymptotics for simple eigenvalues as the poles collapse at an interior point out of nodal lines of the limit eigenfunction.

Keywords: Asymptotics of Eigenvalues; Aharonov–Bohm Operators

MSC 2010: 35P20; 35P15; 35J10

Dedicated to Professor Ireneo Peral on the occasion of his 70th birthday


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About the article

Received: 2016-12-14

Accepted: 2017-01-31

Published Online: 2017-03-18

Published in Print: 2017-05-01

Funding Source: European Research Council

Award identifier / Grant number: 339958

Funding Source: Ministero dell’Istruzione, dell’Università e della Ricerca

Award identifier / Grant number: 201274FYK7_008

The authors have been partially supported by the project ERC Advanced Grant 2013 n. 339958: “Complex Patterns for Strongly Interacting Dynamical Systems – COMPAT”, funded by the European Research Council. V. Felli is partially supported by PRIN-2012-grant n. 201274FYK7_008: “Variational and perturbative aspects of nonlinear differential problems”, funded by the Ministero dell’Istruzione, dell’Università e della Ricerca.

Citation Information: Advanced Nonlinear Studies, Volume 17, Issue 2, Pages 283–296, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2017-0004.

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