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Hyperbolic Mixed Problems for Harmonic Tensors

  • G. F. D. Duff (a1)

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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.

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References

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1. Duff, G. F. D., Harmonic p-tensors on normal hyperbolic Riemannian spaces, Can. J. Math., 5 (1953), 5780.
2. Duff, G. F. D., Differential forms in manifolds with boundary, Ann. Math., 56 (1952), 115127.
3. Duff, G. F. D., A tensor boundary value problem of mixed type, Can. J. Math., 6 (1954), 427440.
4. Duff, G. F. D., The potential theory of coclosed harmonic forms, Can. J. Math., 7 (1955), 126137.
5. Duff, G. F. D., A mixed problem for normal hyperbolic equations, Can. J. Math., 9 (1957), 141160.
6. Hadamard, J., Lectures on Cauchy's Problem (New York, 1952).
7. Krzyzanski, M. and Schauder, J., Quasilineare Differentialgleichungen zweiter ordnung vom hyperbolischen Typus. Gemischte Randwertaufgaben, Studia Math., 6 (1936), 162189.
8. Leray, J., Hyperbolic Differential Equations (Princeton, 1953).
9. Riesz, M., L'intégrale de Riemann-Liouville et le problème de Cauchy, Acta Math., 81 (1949), 1223.
10. Schauder, J., Das Anfcngswertprollem einer quasi-lin earen hyperbolischen Differentialgleichungen, Fund. Math., 24 (1935), 213246.
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Hyperbolic Mixed Problems for Harmonic Tensors

  • G. F. D. Duff (a1)

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