In works in collaboration with Jonathan Di Cosmo on one side and with Søren Fournais, Loïc Le Treust and Nicolas Raymond on the other side, we have studied the semiclassical limit for the stationary magnetic nonlinear Schrödinger equation and for the magnetic Sobolev constants in the strong magnetic field régime, où where the magnetic field does not vanish asymptotically in rescaling of the semiclassical limit.
With Denis Bonheure and Manon Nys, we have proved the symmetry and the asymptotic gaussian decay of groundstates of the magnetic nonlinear Schrödinger equation under a weak constant magnetic field and in the absence of electric field.
Denis Bonheure, Manon Nys and Jean Van Schaftingen, Properties of groundstates of nonlinear Schrödinger equations under a weak constant magnetic field, J. Math. Pures Appl. (9) 124 (2019), 123–168.
doi:10.1016/j.matpur.2018.05.007 DIAL:215071 arXiv:1607.00170
Søren Fournais, Loïc Le Treust, Nicolas Raymond and Jean Van Schaftingen, Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian, J. Math. Soc. Japan 69 (2017), no. 4, 1667–1714.
doi:10.2969/jmsj/06941667 DIAL:191994 hal-01285311 arXiv:1603.02810
Jonathan Di Cosmo and Jean Van Schaftingen, Semiclassical stationary states for nonlinear Schrödinger equations under a strong external magnetic field, J. Differential Equations 259 (2015), no. 2, 596–627.
