The aim of this paper is to establish uniform estimates of the bottom of the spectrum of the Neumann realization of (𝒾∇ + qA)2 on a bounded open set Ω with smooth boundary when |∇ × A| = 1 and q → +∞. This problem was motivated by a question occurring in the theory of liquid crystals and appears also in superconductivity questions in large domains.
@article{1427,
title = {Uniform Spectral Estimates for Families of Schr\"odinger Operators with Magnetic Field of Constant Intensity and Applications},
journal = {CUBO, A Mathematical Journal},
volume = {12},
year = {2010},
language = {en},
url = {http://dml.mathdoc.fr/item/1427}
}
Raymond, Nicolas. Uniform Spectral Estimates for Families of Schrödinger Operators with Magnetic Field of Constant Intensity and Applications. CUBO, A Mathematical Journal, Tome 12 (2010) . http://gdmltest.u-ga.fr/item/1427/