THE MODEL MAGNETIC LAPLACIAN ON WEDGES

Nicolas Popoff (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We study a model Schrödinger operator with constan tmagnetic field on an infinite wedge with natural boundary conditions. This problem is related to the semiclassical magnetic Laplacian on 3d domains with edges. We show that the ground energy is lower than the one coming from the regular part of the wedge and is continuous with respect to the geometry. We provide an upper bound for the ground energy on wedges of small opening. Numerical computations enlighten the theoretical approach.

Mots clés: Schrödinger operator; magnetic field; singular domain; linear eigenvalue problem

Domaines: Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Nicolas Popoff. THE MODEL MAGNETIC LAPLACIAN ON WEDGES. 2013. ⟨hal-00845305v1⟩