On the Leading Term of the Eigenvalue Variation for Aharonov-Bohm Operators with a Moving Pole

@article{Abatangelo2016OnTL,
  title={On the Leading Term of the Eigenvalue Variation for Aharonov-Bohm Operators with a Moving Pole},
  author={Laura Abatangelo and Veronica Felli},
  journal={SIAM J. Math. Analysis},
  year={2016},
  volume={48},
  pages={2843-2868}
}
We study the behavior of certain eigenvalues for magnetic Aharonov-Bohm operators with half-integer circulation and Dirichlet boundary conditions in a planar domain. We analyze the leading term in the Taylor expansion of the eigenvalue function as the pole moves in the interior of the domain, proving that it is a harmonic homogeneous polynomial and determining its exact coefficients. 

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 18 references

Eigenvalues variations for Aharonov-Bohm operators

  • C. Léna
  • Journal of Mathematical Physics 56,
  • 2015
1 Excerpt

On the eigenvalues of Aharonov - Bohm operators with varying poles : pole approaching the boundary of the domain

  • S. Terracini
  • Journal of Mathematical Physics
  • 2015

On the eigenvalues of Aharonov-Bohm operators with varying poles: pole approaching the boundary of the domain, Communications

  • B. Noris, M. Nys, S. Terracini
  • Mathematical Physics,
  • 2015
1 Excerpt

On the eigenvalues of Aharonov-Bohm operators with varying poles

  • V. Bonnaillie-Noël, B. Noris, M. Nys, S. Terracini
  • Analysis and PDE,
  • 2014
3 Excerpts

Hoffmann-Ostenhof, On a magnetic characterization of spectral minimal partitions

  • T. B. Helffer
  • J. Eur. Math. Soc. (JEMS),
  • 2013
1 Excerpt

Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

  • V. Felli, A. Ferrero, S. Terracini
  • J. Eur. Math. Soc. (JEMS),
  • 2011

Functional analysis, Sobolev Spaces and Partial Differential Equations, Universitext

  • H. Brezis
  • 2010

Nodal sets of magnetic Schrödinger operators of Aharonov-Bohm type and energy minimizing partitions, Indiana University

  • B. Noris, S. Terracini
  • Mathematics Journal,
  • 2010
1 Excerpt

Similar Papers

Loading similar papers…