- 01-362 B. Helffer, A. Morame
- Magnetic bottles for the Neumann problem:
curvature effects in the case of dimension 3
(175K, LaTeX 2e)
Oct 10, 01
(auto. generated ps),
of related papers
Abstract. In a previous work, we have analyzed the recent results obtained on
the Neumann realization of the
Schr\"odinger operator in the case of dimension 3 by Lu and Pan.
After presenting a short treatment
of their spectral analysis of key-models,
we show briefly how to implement the techniques of
Helffer-Morame in order to give some localization of the ground state.
This leaves open the question of the localization by
curvature effect which was conjectured
by Bernoff-Sternberg in the case of dimension
$2$ and solved by K. Lu and X-B. Pan, M. del Pino, P.L. Felmer and
P. Sternberg, and ourselves.
We shall now analyze the
curvature effects in the case of dimension 3.