On Aharonov-Bohm Operators with Two Colliding Poles

Laura Abatangelo; Veronica Felli; Corentin Léna

doi:10.1515/ans-2017-0004

On Aharonov-Bohm Operators with Two Colliding Poles

Adv Nonlinear Stud. 2017 May 1;17(2):283-296. doi: 10.1515/ans-2017-0004. Epub 2017 Mar 18.

Authors

Laura Abatangelo¹, Veronica Felli², Corentin Léna³

Affiliations

¹ Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi 55, 20125 Milano, Italy.
² Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, Via Cozzi 55, 20125 Milano, Italy.
³ Dipartimento di Matematica Giuseppe Peano, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy.

Abstract

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: 35J10; 35P15; 35P20; Aharonov–Bohm Operators; Asymptotics of Eigenvalues.

Grants and funding

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.