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A Tensor Boundary Value Problem of Mixed Type

  • G. F. D. Duff (a1)

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The boundary value problems of generalized potential theory on finite Riemannian manifolds may be regarded as extensions of the Dirichlet and Neumann problems for harmonic functions. In the tensor theory there is, in fact, a greater variety of such problems; that is to say, these generalizations from classical potential theory can be made in various ways. We here introduce yet another pair of boundary value problems for the tensor equation of Laplace.

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References

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1. (a) Duff, G. F. D., Differential forms in manifolds with boundary, Ann. Math. 56 (1952), 115–127.
(b) Duff, G. F. D., Boundary value problems associated with the tensor Laplace equation, Can. J. Math., 5 (1953), 196–210.
(c) Duff, G. F. D., A tensor equation of elliptic type, Can. J. Math., 5 (1953), 524–535.
2. Duff, G. F. D. and Spencer, D. C., Harmonic tensors on Riemannian manifolds with boundary, Ann. Math., 56 (1952), 128–156.
3. Giraud, G., Equations et systèmes d'équations où figurent des valeurs principales des intégrales, C. R. Acad. Sci. Paris, 204 (1937), 628–630.
4. Kelvin, Lord, Papers, 4, 13 (Cambridge, 1911).
5. de Rham, G. and Kodaira, K., Harmonie integrals, Mimeographed notes, Institute for Advanced Study (Princeton, 1950).
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A Tensor Boundary Value Problem of Mixed Type

  • G. F. D. Duff (a1)

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