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Main Authors:	Felli, Veronica, Roychowdhury, Prasun, Siclari, Giovanni
Format:	Preprint
Published:	2026
Subjects:	Analysis of PDEs 35J10, 35P20, 35J75
Online Access:	https://arxiv.org/abs/2602.14522
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author	Felli, Veronica Roychowdhury, Prasun Siclari, Giovanni
author_facet	Felli, Veronica Roychowdhury, Prasun Siclari, Giovanni
contents	We study a planar magnetic Schrödinger operator with an Aharonov-Bohm vector potential, under Neumann boundary conditions. Through a gauge transformation, the corresponding eigenvalue problem can be formulated in terms of the Laplacian on a fractured domain, where the fracture lies along the segment connecting the pole to its projection on the boundary. As the pole approaches the boundary, we prove that the eigenvalues converge to those of the Neumann Laplacian and the variation exhibits a logarithmic vanishing rate. In the case of multiple eigenvalues, when the pole approaches a fixed point of the boundary, we observe a splitting phenomenon, with the largest branch separating from the others.
format	Preprint
id	arxiv_https___arxiv_org_abs_2602_14522
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	Magnetic Neumann problems with Aharonov-Bohm potentials: boundary asymptotics of eigenvalues and splitting phenomena Felli, Veronica Roychowdhury, Prasun Siclari, Giovanni Analysis of PDEs 35J10, 35P20, 35J75 We study a planar magnetic Schrödinger operator with an Aharonov-Bohm vector potential, under Neumann boundary conditions. Through a gauge transformation, the corresponding eigenvalue problem can be formulated in terms of the Laplacian on a fractured domain, where the fracture lies along the segment connecting the pole to its projection on the boundary. As the pole approaches the boundary, we prove that the eigenvalues converge to those of the Neumann Laplacian and the variation exhibits a logarithmic vanishing rate. In the case of multiple eigenvalues, when the pole approaches a fixed point of the boundary, we observe a splitting phenomenon, with the largest branch separating from the others.
title	Magnetic Neumann problems with Aharonov-Bohm potentials: boundary asymptotics of eigenvalues and splitting phenomena
topic	Analysis of PDEs 35J10, 35P20, 35J75
url	https://arxiv.org/abs/2602.14522

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