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

Raymond, Nicolas

doi:10.2140/apde.2013.6.1289

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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

DOI: 10.2140/apde.2013.6.1289

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

Received: 5 May 2012

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

Vol. 6, No. 6, 2013