Skip to main content
SpringerLink
Log in

A unique continuation theorem for exterior differential forms on Riemannian manifolds

  • Published:
Arkiv för Matematik

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  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).

    MATH  MathSciNet  Google Scholar 

  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).

    MathSciNet  Google Scholar 

  3. Aronszajn, N., andSmith, K. T., Theory of Bessel potentials. I. Ann. Inst. Fourier, Grenoble,11, 385–475 (1961).

    MATH  MathSciNet  Google Scholar 

  4. Calderon, A. P., Uniqueness in the Cauchy problem for partial differential equations. Am. Journ. Math.,80, 16–36 (1958).

    Article  MATH  MathSciNet  Google Scholar 

  5. Carleman, T., Les fonctions quasi-analytiques. Gauthier-Villars, Paris, 1926.

    MATH  Google Scholar 

  6. —, Sur les systèmes linéaires aux derivées partielles du premier ordre à deux variables. C. R. Paris,197, 471–474 (1933).

    MATH  Google Scholar 

  7. Cordes, H. O., Über die Bestimmtheit der Lösungen elliptischer Differentialgleichungen durch Anfangsvorgaben. Nachr. Akad. Wiss. Göttingen,No. 11, 239–258 (1956).

    MathSciNet  Google Scholar 

  8. Heinz, E., Über die Eindeutigkeit beim Cauchyschen Anfangswertproblem einer elliptischen Differentialgleichung zweiter Ordnung. Nach. Akad. Wiss. Göttingen,1, 1–12 (1955).

    MathSciNet  Google Scholar 

  9. Hörmander, L., On the uniqueness of the Cauchy problem, Math. Scand.,6, 213–225 (1958).

    MATH  MathSciNet  Google Scholar 

  10. —, On the uniqueness of the Cauchy problem. II, Math. Scand.7, 177–190 (1959).

    MATH  MathSciNet  Google Scholar 

  11. Mandelbrojt, S., Séries de Fourier et classes quasi-analytiques de fonctions. Gautheir-Villars, Paris, 1935.

    Google Scholar 

  12. Müller, C., On the behavior of the solutions of the differential equation ΔU=F(x,U) in the neighborhood of a point. Comm. Pure Appl. Math.,7, 505–515 (1954).

    MATH  MathSciNet  Google Scholar 

  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).

    MATH  MathSciNet  Google Scholar 

  14. Rham, G. de, Variétés Différentiables. Hermann, Paris, 1955.

    MATH  Google Scholar 

Download references

Authors
  1. N. Aronszajn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Krzywicki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Szarski
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This paper was written under Contract Nonr 58 304 with the Office of Naval Research.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aronszajn, N., Krzywicki, A. & Szarski, J. A unique continuation theorem for exterior differential forms on Riemannian manifolds. Ark. Mat. 4, 417–453 (1962). https://doi.org/10.1007/BF02591624

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02591624

Keywords

Search

Navigation