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Representation of magnetic fields by jump theorem for harmonic forms
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2-6-20-3 Shiro-machi, Hikone, Shiga 522-0068, Japan.
2008 (English)In: Mathematical Proceedings of the Royal Irish Academy, ISSN 1393-7197, E-ISSN 2009-0021, Vol. 108A, no 1, 7-17 p.Article in journal (Refereed) Published
Abstract [en]

It has previously been shown that a surface current density J on a closed Σ of class C°° in R3 induces a static magnetic field Bj in R3 \ Σ, which has some discontinuity along Σ. In this note, we represent Bj by use of jump theorem for harmonic forms in the case where Σ is of class Οω. We then apply this result to prove the existence of a surface current density J, which induces the nonzero magnetic field Bj such that Bj = 0 inside (or outside) of the domain bounded by Σ in R3. This has previously been called the equilibrium magnetic field for Σ.

Place, publisher, year, edition, pages
Dublin: Royal Irish Academy , 2008. Vol. 108A, no 1, 7-17 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-19559DOI: 10.3318/PRIA.2008.108.1.7OAI: oai:DiVA.org:umu-19559DiVA: diva2:202036
Available from: 2009-03-06 Created: 2009-03-06 Last updated: 2016-11-24Bibliographically approved

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