2 citations · 2 across the 6 of their papers we have counts for
9 papers
On Duclos-Exner's conjecture about waveguides in strong uniform magnetic fields
Enguerrand Bon-Lavigne, Loïc Le Treust, Nicolas Raymond +1
We consider the Dirichlet Laplacian with uniform magnetic field on a curved strip in two dimensions. We give a sufficient condition ensuring the existence of the discrete spectrum…
Low frequency asymptotics and local energy decay for the Schr{ö}dinger equation
Julien Royer
We prove low frequency resolvent estimates and local energy decay for the Schr{ö}dinger equation in an asymptotically Euclidean setting. More precisely, we go beyond the optimal es…
Spectrum of a non-selfadjoint quantum star graph
Gabriel Riviere, Julien Royer
We study the spectrum of a quantum star graph with a non-selfadjoint Robin condition at the central vertex. We first prove that, in the high frequency limit, the spectrum of the Ro…
Absence of embedded eigenvalues for translationally invariant magnetic Laplacians
Nicolas Raymond, Julien Royer
Translationnally invariant bidimensional magnetic Laplacians are considered. Using an improved version of the harmonic approximation, we establish the absence of point spectrum und…
Stability of Standing Waves for a Nonlinear Klein-Gordon Equation with Delta Potentials
Elek Csobo, François Genoud, Masahito Ohta +1
In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish…
Energy decay for the Klein-Gordon equation with highly oscillating damping
Julien Royer
We consider the free Klein-Gordon equation with periodic damping. We show on this simple model that if the usual geometric condition holds then the decay of the energy is uniform w…