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arXiv:1105.4073 [math.AP]AbstractReferencesReviewsResources

Hodge-Helmholtz Decompositions of Weighted Sobolev Spaces in Irregular Exterior Domains with Inhomogeneous and Anisotropic Media

Dirk Pauly

Published 2011-05-20Version 1

We study in detail Hodge-Helmholtz decompositions in non-smooth exterior domains filled with inhomogeneous and anisotropic media. We show decompositions of alternating differential forms belonging to weighted Sobolev spaces into irrotational and solenoidal forms. These decompositions are essential tools, for example, in electro-magnetic theory for exterior domains. In the appendix we translate our results to the classical framework of vector analysis.

Comments: Key Words: Hodge-Helmholtz decompositions, Maxwell's equations, electro-magnetic theory, weighted Sobolev spaces
Journal: Mathematical Methods in the Applied Sciences, 31, (2008), 1509-1543
Categories: math.AP, math-ph, math.DG, math.MP
Subjects: 35Q60, 58A10, 58A14, 78A25, 78A30
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