Peak power in the 3D magnetic Schrödinger equation

Virginie Bonnaillie-Noël (1) , Nicolas Raymond (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

This paper is devoted to the spectral analysis of the magnetic Neumann Laplacian on an infinite cone of aperture $\alpha$. When the magnetic field is constant and parallel to the revolution axis and when the aperture goes to zero, we prove that the first $n$ eigenvalues exist and admit asymptotic expansions in powers of $\alpha^2$.

Mots clés: Magnetic Laplacian; singular 3D domain; spectral asymptotics

Domaines: Equations aux dérivées partielles [math.AP]

Virginie Bonnaillie-Noël, Nicolas Raymond. Peak power in the 3D magnetic Schrödinger equation. Journal of Functional Analysis, 2013, 265 (8), pp.1579-1614. ⟨10.1016/j.jfa.2013.06.014⟩. ⟨hal-00747708v2⟩