JournalsjstVol. 9, No. 2pp. 379–427

Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators

  • Laura Abatangelo

    Università degli Studi di Milano-Bicocca, Italy
  • Veronica Felli

    Università degli Studi di Milano-Bicocca, Italy
  • Luc Hillairet

    Université d’Orléans, France
  • Corentin Léna

    Stockholm University, Sweden
Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators cover

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Abstract

We first establish a sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenvalue variation, as a removed compact set concentrates at that point. Then we apply this spectral stability result to the study of the asymptotic behaviour of eigenvalues of Aharonov–Bohm operators with two colliding poles moving on an axis of symmetry of the domain.

Cite this article

Laura Abatangelo, Veronica Felli, Luc Hillairet, Corentin Léna, Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators. J. Spectr. Theory 9 (2018), no. 2, pp. 379–427

DOI 10.4171/JST/251