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Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |

Home > Vol. 65 > pp. 93-102
## ON UNIQUENESS THEOREM OF A VECTOR FUNCTIONBy X. Zhou
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.
2. Arfken, G. B. and H. J. Weber, 3. Cheng, D. K., 4. Stratton, J. A., 5. O'Rahilly, A., 6. King, R. W. P., 7. Korn, G. A. and T. M. Korn, 8. Weisstein, E. W., 9. Zhou, X. L., "On Helmholtz's theorem and its interpretations," 10. Plonsey, R. and R. E. Collin, 11. Woodside, D. A., "Uniqueness theorems for classical fourvector fields in euclidean and minkowski spaces," 12. Bladel, V., 13. Zhou, X. L., "On independence, completeness of maxwells equations and uniqueness theorems in electromagnetics," 14. Cantarella, J., D. D. Turck, and H. Gluck, "Vector calculus and the topology of domains in 3-space," 15. Schwarz, G., |

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