Diamagnetism versus Robin condition and concentration of ground states

Article type: Research Article

Authors: Kachmar, Ayman

Affiliations: Department of Mathematics, Lebanese University, Hadath, Lebanon. E-mail: ayman.kashmar@gmail.com

Abstract: We estimate the ground state energy for the magnetic Laplacian with a Robin boundary condition. In a special asymptotic limit, we find that the magnetic field does not contribute to the two-term expansion of the ground state energy, thereby proving that the Robin boundary condition weakens diamagnetism. We discuss a semi-classical version of the operator and prove that the ground states concentrate near the boundary points of maximal curvature.

Keywords: magnetic Laplacian, Robin boundary condition, semi-classical analysis

DOI: 10.3233/ASY-161372

Journal: Asymptotic Analysis, vol. 98, no. 4, pp. 341-375, 2016