Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-22T14:26:06.394Z Has data issue: false hasContentIssue false
  • English
  • Français

Hyperbolic Mixed Problems for Harmonic Tensors

Published online by Cambridge University Press:  20 November 2018

G. F. D. Duff
G. F. D. Duff*
Affiliation:
University of Toronto and University of Saskatchewan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper may be regarded as a sequel to (1), where the initial value or Cauchy problem for harmonic tensors on a normal hyperbolic Riemann space was treated. The mixed problems to be studied here involve boundary conditions on a timelike boundary surface in addition to the Cauchy data on a spacelike initial manifold. The components of a harmonic tensor satisfy a system of wave equations with similar principal part, and we assign two initial conditions and one boundary condition for each component.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 161 - 179
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Duff, G. F. D., Harmonic p-tensors on normal hyperbolic Riemannian spaces, Can. J. Math., 5 (1953), 57–80.Google Scholar
2. Duff, G. F. D., Differential forms in manifolds with boundary, Ann. Math., 56 (1952), 115–127.Google Scholar
3. Duff, G. F. D., A tensor boundary value problem of mixed type, Can. J. Math., 6 (1954), 427–440.Google Scholar
4. Duff, G. F. D., The potential theory of coclosed harmonic forms, Can. J. Math., 7 (1955), 126–137.Google Scholar
5. Duff, G. F. D., A mixed problem for normal hyperbolic equations, Can. J. Math., 9 (1957), 141–160.Google Scholar
6. Hadamard, J., Lectures on Cauchy's Problem (New York, 1952).Google Scholar
7. Krzyzanski, M. and Schauder, J., Quasilineare Differentialgleichungen zweiter ordnung vom hyperbolischen Typus. Gemischte Randwertaufgaben, Studia Math., 6 (1936), 162–189.Google Scholar
8. Leray, J., Hyperbolic Differential Equations (Princeton, 1953).Google Scholar
9. Riesz, M., L'intégrale de Riemann-Liouville et le problème de Cauchy, Acta Math., 81 (1949), 1–223.Google Scholar
10. Schauder, J., Das Anfcngswertprollem einer quasi-lin earen hyperbolischen Differentialgleichungen, Fund. Math., 24 (1935), 213–246.Google Scholar