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arXiv · 2207.13627

On the magnetic laplacian with a piecewise constant magnetic field in $\mathbb{R}^3_+$

Emanuela L. Giacomelli
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Abstract

We consider the Neumann realization of the magnetic laplacian in $\mathbb{R}^3_+$, in the case in which the magnetic field has a piecewise constant strength and a uniform direction. This operator is expected to be an effective model in studying the threshold to the normal state for a 3D superconductor exposed to a discontinuous magnetic field. We review some recent results above the infimum of the spectrum of the aforementioned operator.

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Emanuela L. Giacomelli. 2022-07-27. On the magnetic laplacian with a piecewise constant magnetic field in $\mathbb{R}^3_+$. https://arxiv.org/abs/2207.13627

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