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Progress In Electromagnetics Research
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ON UNIQUENESS THEOREM OF A VECTOR FUNCTION

By X. Zhou

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Abstract:
Based on a generalized Helmholtz's identity, definitions of an irrotational vector and a solenoidal vector are reviewed, and new definitions are presented. It is pointed out that the well-known uniqueness theorem of a vector function is incomplete. Although the divergence and curl are specified, for problems with finite boundary surfaces, normal components are not sufficient for uniquely determininga vector function. A complete uniqueness theorem and its two corollaries are then presented. It is proven that a vector function can be uniquely determined by specifyingits divergence and curl in the problem region, its value (both normal and tangential components) on the boundary.

Citation: (See works that cites this article)
X. Zhou, "On Uniqueness Theorem of a Vector Function," Progress In Electromagnetics Research, Vol. 65, 93-102, 2006.
doi:10.2528/PIER06081202
http://www.jpier.org/PIER/pier.php?paper=06081202

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