Strong diamagnetism for the ball in three dimensions

Article type: Research Article

Authors: Fournais, Søren | Persson, Mikael

Affiliations: Department of Mathematical Sciences, Aarhus University, 1530 Ny Munkegade, 8000 Aarhus C, Denmark. E-mails: fournais@imf.au.dk, mickep@imf.au.dk

Abstract: In this paper we give a detailed asymptotic formula for the lowest eigenvalue of the magnetic Neumann Schrödinger operator in the ball in three dimensions with constant magnetic field, as the strength of the magnetic field tends to infinity. This asymptotic formula is used to prove that the eigenvalue is monotonically increasing for large values of the magnetic field.

Keywords: eigenvalue asymptotics, large magnetic field, unit ball, Ginzburg–Landau functional, surface superconductivity

DOI: 10.3233/ASY-2010-1023

Journal: Asymptotic Analysis, vol. 72, no. 1-2, pp. 77-123, 2011