On the semi-classical Neumann Laplacian with variable magnetic field
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Publication:2837173
zbMATH Open1291.35147arXiv0905.3460MaRDI QIDQ2837173
Publication date: 10 July 2013
Published in: Séminaire Équations aux Dérivées Partielles (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/0905.3460
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