Manon Nys

Manon Nys
Università degli Studi di Torino | UNITO · Dipartimento di Matematica "Giuseppe Peano"

PhD

About

10
Publications
657
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98
Citations
Introduction
Additional affiliations
March 2016 - present
Università degli Studi di Torino
Position
  • PostDoc Position
October 2011 - September 2015
Université Libre de Bruxelles
Position
  • PhD Student
October 2011 - September 2015
Università degli Studi di Milano-Bicocca
Position
  • PhD Student

Publications

Publications (10)
Article
Full-text available
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 couples position of the pole-circulation which keep fixed the multiplicity of a double eigenvalue of the operator with the pole at the origin and half-integer circulation....
Article
Full-text available
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...
Article
Full-text available
In this note we consider the action functional $$\begin{aligned} \int _{\mathbb {R}\times \omega } \left( 1 - \sqrt{1 - |\nabla u|^{2}} + W(u) \right) \mathrm {d}\bar{x} \end{aligned}$$where W is a double well potential and \(\omega \) is a bounded domain of \(\mathbb {R}^{N-1}\). We prove existence, one-dimensionality and uniqueness (up to transla...
Article
Full-text available
We study the qualitative properties of groundstates of the time-independent magnetic semilinear Schr\"odinger equation \[ - (\nabla + i A)^2 u + u = |u|^{p-2} u, \qquad \text{ in } \mathbb{R}^N, \] where the magnetic potential $A$ induces a constant magnetic field. When the latter magnetic field is small enough, we show that the groundstate solutio...
Article
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 planar domain. We establish a sharp relation between the rate of convergence of the eigenval-ues as the singular pole is approaching a boundary point and the number of nodal...
Article
Full-text available
In this note we consider the action functional \[ \int_{\mathbb{R} \times \omega} \left( 1 - \sqrt{ 1 - |\nabla u|^2 } + W(u) \right) \, \mathrm{d}t, \] where $W$ is a double well potential and $\omega$ is a bounded domain of $\mathbb{R}^{N-1}$. We prove existence, one-dimensionality and uniqueness (up to translation) of a smooth minimizing phase t...
Article
Full-text available
We consider a magnetic Schrödinger operator with magnetic field concentrated at one point (the pole) of a domain and half integer circulation, and we focus on the behavior of Dirichlet eigenvalues as functions of the pole. Although the magnetic field vanishes almost everywhere, it is well known that it affects the operator at the spectral level (th...
Article
Full-text available
In this paper, we study the semiclassical limit for the stationary magnetic nonlinear Schrödinger equation (i∇ + A(x)) 2 u + V (x)u = |u| p−2 u, x ∈ R 3 , (0.1) where p > 2, A is a vector potential associated to a given magnetic field B, i.e ∇ × A = B and V is a nonnegative, scalar (electric) potential which can be singular at the origin and vanish...
Article
Full-text available
We continue the analysis started in [Noris,Terracini,Indiana Univ Math J,2010] and [Bonnaillie-No\"el,Noris,Nys,Terracini,Analysis & PDE,2014], concerning the behavior of the eigenvalues of a magnetic Schr\"odinger operator of Aharonov-Bohm type with half-integer circulation. We consider a planar domain with Dirichlet boundary conditions and we con...
Article
Full-text available
We consider a magnetic operator of Aharonov-Bohm type with Dirichlet boundary conditions in a planar domain. We analyse the behavior of its eigenvalues as the singular pole moves in the domain. For any value of the circulation we prove that the k-th magnetic eigenvalue converges to the k-th eigenvalue of the Laplacian as the pole approaches the bou...