On the semi-classical 3D Neumann Laplacian with variable magnetic field

2009/05/21 by Nicolas Raymond, Raymond, Nicolas
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0905.3460

openalex publication_date 2009/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we are interested in the semi-classical estimates of the spectrum of the Neumann Laplacian in dimension 3. This work aims to present a complementary case to the one presented in the paper of Helffer and Morame in the case of constant magnetic field. More precisely, in the case when the magnetic field is variable and under the most generic condition for which boundary localizations can be observed, we prove a three terms upper bound for the lowest eigenvalue and establish some semi-classical behaviour of the spectrum.

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