 02145 B. Helffer, A. Morame
 Magnetic bottles for the Neumann problem: curvature effects in the case
of dimension 3 (general case)
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Mar 25, 02

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Abstract. We consider the first eigenvalue e(h) of the Neumann
operator associated to the Laplace operator
with constant magnetic field B,
$(ih\bigtriangledown +B\wedge x/2)^2$,
on a bounded domain.
We show that, as h go to zero, e(h) has an asymptotic
expansion
$e(h)\sim h B\Theta_0 +h^{4/3}B^{2/3}\Theta_1$.
The first constant, $\Theta_0$, is independent
of the domain and the second one, $\Theta_1$, is related
to the curvature of the boundary, on
the curve where the magnetic field
is tangent to the boundary.
This paper is an extension of the previous
preprint mp_arc 01362 and gives a complete proof
in the general generic case.
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