Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells (Q1915343)

Motivated by a recent paper by \textit{R. Montgomery} [Commun. Math. Phys. 168, No. 3, 651-675 (1995; Zbl 0827.58076)], we give the asymptotic behavior, in the semi-classical sense, of the ground state energy for the Schrödinger 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 a hypersurface or a finite union of points.