A unique continuation theorem for exterior differential forms on Riemannian manifolds. (English) Zbl 0107.07803

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[1] Aronszajn, N., Sur l’unicité du prolongement des solutions des équations aux dérivées partielles elliptiques du second ordre. C. R. Paris,242, 723–725 (1956). · Zbl 0074.31203
[2] –, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. Journ. Math. Pures et Appliquées,36, 235–249, (1957). · Zbl 0084.30402
[3] Aronszajn, N., andSmith, K. T., Theory of Bessel potentials. I. Ann. Inst. Fourier, Grenoble,11, 385–475 (1961). · Zbl 0102.32401
[4] Calderon, A. P., Uniqueness in the Cauchy problem for partial differential equations. Am. Journ. Math.,80, 16–36 (1958). · Zbl 0080.30302 · doi:10.2307/2372819
[5] Carleman, T., Les fonctions quasi-analytiques. Gauthier-Villars, Paris, 1926.
[6] –, Sur les systèmes linéaires aux derivées partielles du premier ordre à deux variables. C. R. Paris,197, 471–474 (1933).
[7] Cordes, H. O., Über die Bestimmtheit der Lösungen elliptischer Differentialgleichungen durch Anfangsvorgaben. Nachr. Akad. Wiss. Göttingen,No. 11, 239–258 (1956). · Zbl 0074.08002
[8] Heinz, E., Über die Eindeutigkeit beim Cauchyschen Anfangswertproblem einer elliptischen Differentialgleichung zweiter Ordnung. Nach. Akad. Wiss. Göttingen,1, 1–12 (1955). · Zbl 0067.07503
[9] Hörmander, L., On the uniqueness of the Cauchy problem, Math. Scand.,6, 213–225 (1958). · Zbl 0088.30201
[10] –, On the uniqueness of the Cauchy problem. II, Math. Scand.7, 177–190 (1959). · Zbl 0090.08001
[11] Mandelbrojt, S., Séries de Fourier et classes quasi-analytiques de fonctions. Gautheir-Villars, Paris, 1935. · Zbl 0013.11006
[12] Müller, C., On the behavior of the solutions of the differential equation {\(\Delta\)}U=F(x,U) in the neighborhood of a point. Comm. Pure Appl. Math.,7, 505–515 (1954). · Zbl 0056.32201 · doi:10.1002/cpa.3160070304
[13] Pederson, R. N., On the unique continuation theorem for certain second and fourth order elliptio equations, Comm. Pure Appl. Math.,11, 67–80 (1958). · Zbl 0080.30703 · doi:10.1002/cpa.3160110104
[14] Rham, G. de, Variétés Différentiables. Hermann, Paris, 1955.
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