Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Electromagnetic field in the source region of continuously varying current density


Author: John G. Fikioris
Journal: Quart. Appl. Math. 54 (1996), 201-209
MSC: Primary 78A25
DOI: https://doi.org/10.1090/qam/1388012
MathSciNet review: MR1388012
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Abstract: Continuity, analyticity, and the singular points of the vector potential A and the field vectors H, E in a spherical source region $ \nu $ are investigated thoroughly for, practically, any continuous current density distribution J in $ \nu $. In other words, this is a study of the inhomogeneous Helmholtz equation in $ \nu $. Explicit results for A, H, E are obtained by direct integration, extending previous results for constant density in $ \nu $ to continuously varying ones. The importance of imposing the Hölder condition on J to insure existence of E and of certain second derivatives of A is explicitly demonstrated by a specific continuous J, violating this condition at a point; it is then seen that E and some second derivatives of A do not exist, tending to infinity, at that point.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/qam/1388012
Article copyright: © Copyright 1996 American Mathematical Society

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