Semiclassical Analysis for the Ground State Energy of a Schrِdinger Operator with Magnetic Wells

Motivated by a recent paper by Montgomery [Mon], we give the asymptotic behavior, in the semi-classical sense, of the ground state energy for the Schrِdinger operator with a magnetic field. We consider the case when the locus of the minima of the intensity of the magnetic field is compact and our study is sharper when this locus is an hypersurface or a finite union of points