Laura Abatangelo

Singularity of eigenfunctions at the junction of shrinking tubes, Part II

In continuation with the paper arXiv:1202.4414, we investigate the asymptotic behavior of weighted eigenfunctions in two half-spaces connected by a thin tube. We provide several improvements about some convergences stated in arXiv:1202.4414; most of all, we provide the exact asymptotic behavior of the implicit normalization for solutions given in arXiv:1202.4414 and thus describe the (N-1)-order singularity developed at a junction of the tube (where N is the space dimension).

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

We study the behavior of eigenvalues for magnetic Aharonov-Bohm operators with half-integer circulation and Dirichlet boundary conditions in a planar domain. We analyse 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 detecting its exact coefficients.

On Aharonov-Bohm Operators with Two Colliding Poles

Abstract We consider Aharonov–Bohm operators with two poles and prove sharp asymptotics for simple eigenvalues as the poles collapse at an interior point out of nodal lines of the limit eigenfunction.

Rate of convergence for eigenfunctions of Aharonov-Bohm operators with a moving pole

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.

Estimates for eigenvalues of Aharonov–Bohm operators with varying poles and non-half-integer circulation

We study the behavior of eigenvalues of a magnetic Aharonov-Bohm operator with non-half-integer circulation and Dirichlet boundary conditions in a planar domain. As the pole is moving in the interior of the domain, we estimate the rate of the eigenvalue variation in terms of the vanishing order of the limit eigenfunction at the limit pole. We also provide an accurate blow-up analysis for scaled eigenfunctions and prove a sharp estimate for their rate of convergence.