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The Analysis and Geometry of Hardy's Inequality pp 165–212Cite as

Inequalities and Operators Involving Magnetic Fields

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Abstract

In classical mechanics the motion of charged particles depends only on electric and magnetic fields E, B which are uniquely described by Maxwell’s equations:

$$\displaystyle{\nabla \cdot \mathbf{E} = 4\pi \rho,}$$
$$\displaystyle{\nabla \cdot \mathbf{B} = 0,}$$
$$\displaystyle{\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t},}$$
$$\displaystyle{\nabla \times \mathbf{B} = 4\pi \mathbf{J} + \frac{\partial \mathbf{E}} {\partial t}.}$$

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Authors and Affiliations

  1. School of Mathematics, Cardiff University, Cardiff, UK

    Alexander A. Balinsky & W. Desmond Evans

  2. Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama, USA

    Roger T. Lewis

Authors
  1. Alexander A. Balinsky
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  2. W. Desmond Evans
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  3. Roger T. Lewis
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Balinsky, A.A., Evans, W.D., Lewis, R.T. (2015). Inequalities and Operators Involving Magnetic Fields. In: The Analysis and Geometry of Hardy's Inequality. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-22870-9_5

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