On a Poisson's equation arising from magnetism

Luca Lussardi

doi:10.3934/dcdss.2015.8.769

Article Contents

2015, Volume 8, Issue 4: 769-772. Doi: 10.3934/dcdss.2015.8.769

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On a Poisson's equation arising from magnetism

Luca Lussardi^1,

1.
Dipartimento di Matematica e Fisica "N.Tartaglia", Università Cattolica del Sacro Cuore, Via dei Musei 41, I-25121 Brescia

Received: December 31, 2013

Revised: June 30, 2014

Published: July 2015

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Abstract

We review the proof of existence and uniqueness of the Poisson's equation $\Delta u + {\rm div}\,{\bf m}=0$ whenever ${\bf m}$ is a unit $L^2$-vector field on $\mathbb R^3$ with compact support; by standard linear potential theory we deduce also the $H^1$-regularity of the unique weak solution.

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Mathematics Subject Classification: Primary: 35J05; Secondary: 3101.

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References

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