FOURNAIS, Soeren - Analyse Numérique et E.D.P., Université Paris-Sud, Bât. 425, 91405 Orsay cedex
HELFFER, Bernard - Analyse Numérique et E.D.P., Université Paris-Sud, Bât. 425, 91405 Orsay cedex

Abstract :

Motivated by the theory of superconductivity and more precisely by the problem of the onset of superconductivity in dimension two, many papers devoted to the analysis in a semi-classical regime of the lowest eigenvalue of the Schrodinger operator with magnetic field have appeared recently. Here we would like to mention the works by Bernoff-Sternberg, Lu-Pan, Del Pino-Felmer-Sternberg and Helffer-Morame and also Bauman-Phillips-Tang for the case of a disc. In the present paper we settle one important part of this question completely by proving an asymptotic expansion to all orders for low-lying eigenvalues for generic domains. The word `generic' means in this context that the curvature of the boundary of the domain has a unique non-degenerate maximum.

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Contact : Soeren.Fournais@math.u-psud.fr