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On Uniqueness Theorem of a Vector Function

By Xingling Zhou
Progress In Electromagnetics Research, Vol. 65, 93-102, 2006


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.


 (See works that cites this article)
Xingling Zhou, "On Uniqueness Theorem of a Vector Function," Progress In Electromagnetics Research, Vol. 65, 93-102, 2006.


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