Free Access
Volume 26, 2020
Article Number 39
Number of page(s) 47
Published online 25 June 2020
  1. L. Abatangelo and V. Felli, Sharp asymptotic estimates for eigenvalues of Aharonov-Bohm operators with varying poles. Calc. Var. Partial Differ. Equ. 54 (2015) 3857–3903. [Google Scholar]
  2. L. Abatangelo and V. Felli, On the leading term of the eigenvalue variation for Aharonov-Bohm operators with a moving pole. SIAM J. Math. Anal. 48 (2016) 2843–2868. [CrossRef] [Google Scholar]
  3. L. Abatangelo, V. Felli, L. Hillairet and C. Lena, Spectral stability under removal of small capacity sets and applications to Aharonov-Bohm operators. J. Spectr. Theory 9 (2019) 379–427. [CrossRef] [Google Scholar]
  4. L. Abatangelo, V. Felli and C. Léna, On Aharonov-Bohm operators with two colliding poles. Adv. Nonlin. Stud. 17 (2017) 283–296. [CrossRef] [Google Scholar]
  5. L. Abatangelo, V. Felli, B. Noris and M. Nys, Sharp boundary behavior of eigenvalues for Aharonov-Bohm operators with varying poles. J. Funct. Anal. 273 (2017) 2428–2487. [Google Scholar]
  6. V. Bonnaillie–Noël, B. Helffer and T. Hoffmann-Ostenhof, Aharonov–Bohm Hamiltonians, isospectrality and minimal partitions. J. Phys. A 42 (2009) 185203. [CrossRef] [Google Scholar]
  7. V. Bonnaillie-Noël, B. Noris, M. Nys and S. Terracini, Aharonov-Bohm operators with varying poles. Anal. Partial Differ. Equ. 7 (2014) 1365–1395. [Google Scholar]
  8. E. Colorado and I. Peral, Semilinear elliptic problems with mixed Dirichlet–Neumann boundary conditions. J. Funct. Anal. 199 (2003) 468–507. [Google Scholar]
  9. M.M. Fall, V. Felli, A. Ferrero and A. Niang, Asymptotic expansions and unique continuation at Dirichlet–Neumann boundary junctions for planar elliptic equations. Math. Eng. 1 (2018) 84–117. [CrossRef] [Google Scholar]
  10. V. Felli and A. Ferrero, Almgren-type monotonicity methods for the classification of behaviour at corners of solutions to semilinear elliptic equations. Proc. Roy. Soc. Edinburgh Sect. A 143 (2013) 957–1019. [CrossRef] [Google Scholar]
  11. V. Felli, A. Ferrero and S. Terracini, Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential. J. Eur. Math. Soc. 13 (2011) 119–174. [CrossRef] [Google Scholar]
  12. R.R. Gadyl’shin, Splitting of a multiple eigenvalue of the Dirichlet problem for the Laplace operator under singular perturbation of the boundary condition. (Russian) Mat. Zametki 52 (1992) 42–55; Translation in Math. Notes 52 (1993) 1020–1029. [Google Scholar]
  13. M. Kassmann and W.R. Madych, Difference quotients and elliptic mixed boundary value problems of second order. Indiana Univ. Math. J. 56 (2007) 1047–1082. [CrossRef] [Google Scholar]
  14. A. Laptev and T. Weidl, Hardy inequalities for magnetic Dirichlet forms. In Mathematical results in quantum mechanics (Prague, 1998). Vol. 108 of Oper. Theory Adv. Appl. Birkhäuser, Basel (1999) 299–305. [Google Scholar]
  15. C. Léna, Eigenvalues variations for Aharonov-Bohm operators. J. Math. Phys. 56 (2015) 011502. [Google Scholar]
  16. B. Noris and S. Terracini, Nodal sets of magnetic Schrödinger operators of Aharonov-Bohm type and energy minimizing partitions. Indiana Univ. Math. J. 59 (2010) 1361–1403. [CrossRef] [Google Scholar]
  17. B. Noris, M. Nys and S. Terracini, On the Aharonov–Bohm operators with varying poles: the boundary behavior of eigenvalues. Commun. Math. Phys. 339 (2015) 1101–1146. [CrossRef] [Google Scholar]
  18. M. Reed and B. Simon, Methods of Modern Mathematical Physics. I. Functional Analysis, 2nd edn. Academic Press, New York (1980). [Google Scholar]
  19. G. Savaré, Regularity and perturbation results for mixed second order elliptic problems. Comm. Partial Differ. Equ. 22 (1997) 869–899. [CrossRef] [Google Scholar]
  20. L. Tartar, An introduction to Sobolev spaces and interpolation spaces. Vol. 3 of Lecture Notes of the Unione Matematica Italiana. Springer/UMI, Berlin/Bologna (2007). [Google Scholar]
  21. G.N. Watson, A treatise on the theory of the Bessel functions. Cambridge University Press (1944). [Google Scholar]

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