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Pré-Publication, Document De Travail Année : 2021

MAGNETIC PERTURBATIONS OF THE ROBIN LAPLACIAN IN THE STRONG COUPLING LIMIT

Résumé

This paper is devoted to the asymptotic analysis of the eigenvalues of the Laplace operator with a uniform magnetic field and Robin boundary condition on a smooth planar domain. We show how the singular limit when the Robin parameter tends to infinity is equivalent to a semi-classical limit involving a small positive parameter h (the semi-classical parameter). The main result is a comparison between the spectrum of the Robin Laplacian with an effective operator defined on the boundary of the domain via the Born-Oppenheimer approximation. More precisely, the n-th eigenvalue of the Robin Laplacian is approximated, modulo O(h 2), by the n-th eigenvalue of the effective operator. When the curvature has a unique non-degenerate maximum, the eigenvalue asymptotics displays the contribution of the magnetic field explicitly.
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Dates et versions

hal-03410740 , version 1 (01-11-2021)
hal-03410740 , version 2 (12-11-2021)
hal-03410740 , version 3 (04-02-2022)
hal-03410740 , version 4 (01-05-2023)

Identifiants

  • HAL Id : hal-03410740 , version 1

Citer

Rayan Fahs. MAGNETIC PERTURBATIONS OF THE ROBIN LAPLACIAN IN THE STRONG COUPLING LIMIT. 2021. ⟨hal-03410740v1⟩
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