Vol. 6, No. 6, 2013

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From the Laplacian with variable magnetic field to the electric Laplacian in the semiclassical limit

Nicolas Raymond

Vol. 6 (2013), No. 6, 1289–1326
Abstract

We consider a twisted magnetic Laplacian with Neumann condition on a smooth and bounded domain of ${ℝ}^{2}$ in the semiclassical limit $h\to 0$. Under generic assumptions, we prove that the eigenvalues admit a complete asymptotic expansion in powers of ${h}^{1∕4}$.

Keywords
semiclassical analysis, magnetic field, normal form
Mathematical Subject Classification 2010
Primary: 35J10, 35P15
Milestones
Revised: 2 August 2012
Accepted: 18 October 2012
Published: 18 November 2013
Authors
 Nicolas Raymond Institut de recherche mathématique de Rennes Université de Rennes 1 35042 Rennes Cedex France