12 citations · 27 across the 22 of their papers we have counts for
25 papers
Qualitative properties of eigenfunctions in domains with small holes
Laura Abatangelo, Massimo Grossi, Ying Li
In this paper we study qualitative properties of the eigenvalues and eigenfunctions of with Dirichlet boundary condition in a smooth bounded domain with a small circular h…
Corrigendum to "Ramification of multiple eigenvalues for the Dirichlet-Laplacian in perforated domains" published in Journal of Functional Analysis 283 (2022) 109718
Laura Abatangelo, Corentin Léna, Paolo Musolino
We fix the proof of Theorem 1.17 in the quoted reference, which does not in general gives the correct coefficients in the asymptotic behavior of eigenvalues for the Dirichlet Lapla…
Bifurcation of double eigenvalues for Aharonov-Bohm operators with a moving pole
Laura Abatangelo, Veronica Felli
We study double eigenvalues of Aharonov-Bohm operators with Dirichlet boundary conditions in planar domains containing the origin. We focus on the behavior of double eigenvalues wh…
On solutions to a class of degenerate equations with the Grushin operator
Laura Abatangelo, Alberto Ferrero, Paolo Luzzini
The Grushin Laplacian is a degenerate elliptic operator in that degenerates on . We consider weak solutions of in…
Asymptotic behavior of generalized capacities with applications to eigenvalue perturbations: the higher dimensional case
Laura Abatangelo, Corentin Léna, Paolo Musolino
We provide a full series expansion of a generalization of the so-called -capacity related to the Dirichlet-Laplacian in dimension three and higher, extending previous results of…
Sharp behavior of Dirichlet--Laplacian eigenvalues for a class of singularly perturbed problems
Laura Abatangelo, Roberto Ognibene
We deepen the study of Dirichlet eigenvalues in bounded domains where a thin tube is attached to the boundary. As its section shrinks to a point, the problem is spectrally stable a…
Ramification of multiple eigenvalues for the Dirichlet-Laplacian in perforated domains
Laura Abatangelo, Corentin Léna, Paolo Musolino
Taking advantage from the so-called "Lemma on small eigenvalues" by Colin de Verdière, we study ramification for multiple eigenvalues of the Dirichlet Laplacian in bounded perforat…
Asymptotic behavior of -capacities and singular perturbations for the Dirichlet-Laplacian
Laura Abatangelo, Virginie Bonnaillie-Noël, Corentin Léna +1
In this paper we study the asymptotic behavior of -capacities of small sets and its application to the analysis of the eigenvalues of the Dirichlet-Laplacian on a bounded planar…
On simple eigenvalues of the fractional Laplacian under removal of small fractional capacity sets
Laura Abatangelo, Veronica Felli, Benedetta Noris
We consider the eigenvalue problem for the restricted fractional Laplacian in a bounded domain with homogeneous Dirichlet boundary conditions. We introduce the notion of fractional…
Eigenvalue variation under moving mixed Dirichlet-Neumann boundary conditions and applications
Laura Abatangelo, Veronica Felli, Corentin Léna
We deal with the sharp asymptotic behaviour of eigenvalues of elliptic operators with varying mixed Dirichlet-Neumann boundary conditions. In case of simple eigenvalues, we compute…
Multiple Aharonov--Bohm eigenvalues: the case of the first eigenvalue on the disk
Laura Abatangelo
It is known that the first eigenvalue for Aharonov--Bohm operators with half-integer circulation in the unit disk is double if the potential's pole is located at the origin. We pro…
On multiple eigenvalues for Aharonov-Bohm operators in planar domains
Laura Abatangelo, Manon Nys
We study multiple eigenvalues of a magnetic Aharonov-Bohm operator with Dirichlet boundary conditions in a planar domain. In particular, we study the structure of the set of the co…
Estimates for eigenvalues of Aharonov-Bohm operators with varying poles and non-half-interger circulation
Laura Abatangelo, Veronica Felli, Benedetta Noris +1
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 mov…
On Aharonov-Bohm operators with two colliding poles
Laura Abatangelo, Veronica Felli, Corentin Lena
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 eig…
Rate of convergence for eigenfunctions of Aharonov-Bohm operators with a moving pole
Laura Abatangelo, Veronica Felli
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 es…
Spectral stability under removal of small capacity sets and applications to Aharonov-Bohm operators
Laura Abatangelo, Veronica Felli, Luc Hillairet +1
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 eigenva…
Sharp boundary behavior of eigenvalues for Aharonov-Bohm operators with varying poles
Laura Abatangelo, Veronica Felli, Benedetta Noris +1
In this paper, we investigate the behavior of the eigenvalues of a magnetic Aharonov-Bohm operator with half-integer circulation and Dirichlet boundary conditions in a bounded plan…
On the leading term of the eigenvalue variation for Aharonov-Bohm operators with a moving pole
Laura Abatangelo, Veronica Felli
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…
Sharp asymptotic estimates for eigenvalues of Aharonov-Bohm operators with varying poles
Laura Abatangelo, Veronica Felli
We investigate the behavior of eigenvalues for a magnetic Aharonov-Bohm operator with half-integer circulation and Dirichlet boundary conditions in a planar domain. We provide shar…
On the sharp effect of attaching a thin handle on the spectral rate of convergence
Laura Abatangelo, Veronica Felli, Susanna Terracini
Consider two domains connected by a thin tube: it can be shown that the resolvent of the Dirichlet Laplacian is continuous with respect to the channel section parameter. This in pa…
Singularity of eigenfunctions at the junction of shrinking tubes, Part II
Laura Abatangelo, Veronica Felli, Susanna Terracini
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 im…
Positive harmonic functions in union of chambers
Laura Abatangelo, Susanna Terracini
We characterize the set of positive harmonic functions with Dirichlet boundary conditions in unbounded domains which are union of several different chambers. We analyze the asympto…
Singularity of eigenfunctions at the junction of shrinking tubes. Part I
Veronica Felli, Susanna Terracini
Consider two domains connected by a thin tube: it can be shown that, generically, the mass of a given eigenfunction of the Dirichlet Laplacian concentrates in only one of them. The…
Solutions to nonlinear Schrödinger equations with singular electromagnetic potential and critical exponent
Laura Abatangelo, Susanna Terracini
We investigate existence and qualitative behaviour of solutions to nonlinear Schrödinger equations with critical exponent and singular electromagnetic potentials. We are concerned…