This paper is devoted to the symmetry and symmetry breaking properties of a two-dimensional magnetic Schrödinger operator involving an Aharonov–Bohm magnetic vector potential. We investigate the symmetry properties of the optimal potential for the corresponding magnetic Keller–Lieb–Thirring inequality. We prove that this potential is radially symmetric if the intensity of the magnetic field is below an explicit threshold, while symmetry is broken above a second threshold corresponding to a higher magnetic field. The method relies on the study of the magnetic kinetic energy of the wave function and amounts to study the symmetry properties of the optimal functions in a magnetic Hardy–Sobolev interpolation inequality. We give a quantified rang...
AbstractHardy and Sobolev-type inequalities in Lp(Rn),1<p<∞,n⩾2, associated with magnetic fields, ar...
We study the magnetic Schrodinger operator $H$ on $\textbf{\textit{R}}^n$, $n\geq3$. We assume that ...
We obtained the approximate two-dimensional bound states solutions of a Klein–Gordon particle moving...
International audienceThis paper is devoted to the symmetry and symmetry breaking properties of a tw...
This paper is devoted to a collection of results on nonlinear interpolation inequalities associated ...
We explicitly compute the spectrum and eigenfunctions of the magnetic Schrödinger operator H(A→,V)=(...
International audienceWe study functional and spectral properties of perturbations of the magnetic L...
The Aharonov–Bohm Hamiltonian is the energy operator which governs quantum particles moving in a sol...
The diamagnetic inequality is established for the Schr\uf6dinger operator H 0 (d) in L 2 (ℝ d ), d ...
The diamagnetic inequality is established for the Schrödinger operator H (d) 0 in L 2 (Rd), d=2,3, d...
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of s...
For a Schrödinger operator on the plane R2 with electric potential V and an Aharonov–Bohm magnetic f...
In this article, we introduce a notion of magnetic field in the Heisenberg group and we study its in...
We first prove a weighted inequality of Moser-Trudinger type depending on a parameter, in the two-di...
We study the spectrum of the Schroedinger operator for a particle constrained on a two-dimensional f...
AbstractHardy and Sobolev-type inequalities in Lp(Rn),1<p<∞,n⩾2, associated with magnetic fields, ar...
We study the magnetic Schrodinger operator $H$ on $\textbf{\textit{R}}^n$, $n\geq3$. We assume that ...
We obtained the approximate two-dimensional bound states solutions of a Klein–Gordon particle moving...
International audienceThis paper is devoted to the symmetry and symmetry breaking properties of a tw...
This paper is devoted to a collection of results on nonlinear interpolation inequalities associated ...
We explicitly compute the spectrum and eigenfunctions of the magnetic Schrödinger operator H(A→,V)=(...
International audienceWe study functional and spectral properties of perturbations of the magnetic L...
The Aharonov–Bohm Hamiltonian is the energy operator which governs quantum particles moving in a sol...
The diamagnetic inequality is established for the Schr\uf6dinger operator H 0 (d) in L 2 (ℝ d ), d ...
The diamagnetic inequality is established for the Schrödinger operator H (d) 0 in L 2 (Rd), d=2,3, d...
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of s...
For a Schrödinger operator on the plane R2 with electric potential V and an Aharonov–Bohm magnetic f...
In this article, we introduce a notion of magnetic field in the Heisenberg group and we study its in...
We first prove a weighted inequality of Moser-Trudinger type depending on a parameter, in the two-di...
We study the spectrum of the Schroedinger operator for a particle constrained on a two-dimensional f...
AbstractHardy and Sobolev-type inequalities in Lp(Rn),1<p<∞,n⩾2, associated with magnetic fields, ar...
We study the magnetic Schrodinger operator $H$ on $\textbf{\textit{R}}^n$, $n\geq3$. We assume that ...
We obtained the approximate two-dimensional bound states solutions of a Klein–Gordon particle moving...