- 00-452 Bernard Helffer and Abderemane Morame
- Magnetic bottles in connection with superconductivity
Nov 13, 00
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of related papers
Abstract. 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
of the lowest eigenvalue of the
with magnetic field have appeared
recently. Here we would like to mention the works by
Bernoff-Sternberg, Lu-Pan and Del Pino-Felmer-Sternberg.
partially questions analyzed in a different context
by the authors around the question of the so called magnetic bottles.
is to analyze the former results, to treat them in a more
and to improve them by giving sharper estimates
of the remainder. In particular,
we improve significatively the lower bounds
and as a byproduct 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.