Magnetic bottles in connection with superconductivity

摘要

Motivated by the theory of superconductivity and more precisely by the problem of the onset of superconductivity in dimension two, a lot of papers devoted to the analysis in a semi-classical regime of the lowest eigenvalue of the Schrodinger operator with magnetic field have appeared recently. Here we mention the works by Bernoff-Sternberg, Lu-Pan and Del Pino Felmer-Sternberg. This partially recovers questions analyzed in a different context by the authors around the question of the so called magnetic bottles. Our aim is to analyze the former results, to treat them in a more systematic way and to improve them by giving sharper estimates of the remainder. In particular, we improve significantly the lower bounds and as a by-product we solve a conjecture proposed by Bernoff Sternberg concerning the localization of the ground state inside the boundary in the case with constant magnetic fields. (C) 2001 Academic Press. [References: 57]