56 citations · 305 across the 37 of their papers we have counts for
5 papers · 1 filter
Strong confinement limit for the nonlinear Schrödinger equation constrained on a curve
Florian Méhats, Nicolas Raymond
This paper is devoted to the cubic nonlinear Schrödinger equation in a two dimensional waveguide with shrinking cross section of order . For a Cauchy data living essentially on…
Spectral asymptotics of the Dirichlet Laplacian in a conical layer
Monique Dauge, Thomas Ourmières-Bonafos, Nicolas Raymond
The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture l…
Optimal magnetic Sobolev constants in the semiclassical limit
Soeren Fournais, Nicolas Raymond
This paper is devoted to the semiclassical analysis of the best constants in the magnetic Sobolev embeddings in the case of a bounded domain of the plane carrying Dirichlet conditi…
Little Magnetic Book
Nicolas Raymond
This book is devoted to the spectral analysis of the magnetic Laplacian in various geometric situations. In particular the influence of the geometry on the discrete spectrum is ana…
Magnetic WKB Constructions
Virginie Bonnaillie-Noël, Nicolas Raymond, Frédéric Hérau
This paper is devoted to the semiclassical magnetic Laplacian. Until now WKB expansions for the eigenfunctions were only established in presence of a non-zero electric potential. H…