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

  • Laura Abatangelo
  • Veronica FelliEmail author
Part of the Springer INdAM Series book series (SINDAMS, volume 22)


We study the behavior of eigenfunctions for magnetic Aharonov-Bohm operators with half-integer 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.


Aharonov-Bohm potential Convergence of eigenfunctions Magnetic Schrödinger operators 

2010 AMS Classification

35J10 35Q40 35J75 



This paper is dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. The authors have been partially supported by the project ERC Advanced Grant 2013 n. 339958: “Complex Patterns for Strongly Interacting Dynamical Systems—COMPAT”. V. Felli has been partially supported by PRIN-2012-grant “Variational and perturbative aspects of nonlinear differential problems”.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di Milano BicoccaMilanoItaly
  2. 2.Dipartimento di Scienza dei MaterialiUniversità di Milano BicoccaMilanoItaly

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