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A Tensor Equation of Elliptic Type

Published online by Cambridge University Press:  20 November 2018

G. F. D. Duff
G. F. D. Duff*
Affiliation:
University of Toronto
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The theory of the systems of partial differential equations which arise in connection with the invariant differential operators on a Riemannian manifold may be developed by methods based on those of potential theory. It is therefore natural to consider in the same context the theory of elliptic differential equations, in particular those which are self-adjoint. Some results for a tensor equation in which appears, in addition to the operator Δ of tensor theory, a matrix or double tensor field defined on the manifold, are here presented. The equation may be written

in a notation explained below.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 524 - 535
Copyright
Copyright © Canadian Mathematical Society 1953

References

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