We consider the eigenvalues of the magnetic Laplacian on a bounded domain Ω of R2 with uniform magnetic field β>0 and magnetic Neumann boundary conditions. We find upper and lower bounds for the ground state energy λ1 and we provide semiclassical estimates in the spirit of Kröger for the first Riesz mean of the eigenvalues. We also discuss upper bounds for the first eigenvalue for non-constant magnetic fields β=β(x) on a simply connected domain in a Riemannian surface. In particular: we prove the upper bound λ1
Geometric bounds for the magnetic Neumann eigenvalues in the plane / Colbois, B.; Lena, C.; Provenzano, L.; Savo, A.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 179:(2023), pp. 454-497. [10.1016/j.matpur.2023.09.014]
Geometric bounds for the magnetic Neumann eigenvalues in the plane
Provenzano L.
;Savo A.
2023
Abstract
We consider the eigenvalues of the magnetic Laplacian on a bounded domain Ω of R2 with uniform magnetic field β>0 and magnetic Neumann boundary conditions. We find upper and lower bounds for the ground state energy λ1 and we provide semiclassical estimates in the spirit of Kröger for the first Riesz mean of the eigenvalues. We also discuss upper bounds for the first eigenvalue for non-constant magnetic fields β=β(x) on a simply connected domain in a Riemannian surface. In particular: we prove the upper bound λ1| File | Dimensione | Formato | |
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