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.
Abatangelo, L., Felli, V. (2016). On the leading term of the eigenvalue variation for Aharonov-Bohm operators with a moving pole. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 48(4), 2843-2868 [10.1137/15M1044898].
On the leading term of the eigenvalue variation for Aharonov-Bohm operators with a moving pole
ABATANGELO, LAURA;FELLI, VERONICA
2016
Abstract
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.
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