Advertisement

Mathematische Zeitschrift

, Volume 220, Issue 1, pp 561–568 | Cite as

A non uniqueness result for operators of principal type

  • S. Alinhac
  • M. S. Baouendi
Article

Keywords

Cauchy Problem Geometrical Optic Principal Symbol Principal Type Linear Partial Differential Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alinhac, S.: Non unicité du problème de Cauchy. Annals of Math.117, 77–108 (1983)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Alinhac, S., Baouendi, M.S.: Construction de solutions nulles et singulières pour des opérateurs de type principal. Seminaire Goulaouic-Schwartz, exposé no 22, Ecole Polytechnique, Paris 1979Google Scholar
  3. 3.
    Bahouri, H.: Non unicité du problème de Cauchy pour des opérateurs à symbole principal réel. Comm. PDE8 (14), 1521–1547 (1983)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Cohen, P.: The non uniqueness of the Cauchy Problem. ONR Techn. Report 93. Stanford U. 1960Google Scholar
  5. 5.
    Hörmander, L.: Non Uniqueness for the Cauchy Problem. Lect. Notes in Math.,459, 36–72, Springer Verlag (1975)Google Scholar
  6. 6.
    Hörmander, L.: The Analysis of Linear Partial Differential Operators. Berlin: Springer Verlag 1983Google Scholar
  7. 7.
    Hörmander, L.: Linear Partial Differential Operators. Berlin: Springer Verlag 1963zbMATHGoogle Scholar
  8. 8.
    Lerner, N., Robbiano, L.: Unicité de Cauchy pour des opérateurs de type principal. J. d'Analyse Math.44, 32–66 (1984)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Métivier, G.: Counter examples to Holmgren's uniqueness for analytic non linear Cauchy problems. Inv. Math.112, 217–222 (1993)zbMATHCrossRefGoogle Scholar
  10. 10.
    Métivier, G.: Uniqueness and approximation of solutions of first order non linear equations. Invent. Math.82, 262–282 (1985)CrossRefGoogle Scholar
  11. 11.
    Pliš, A.: A smooth linear elliptic differential equation without any solution in a sphere. Comm. Pure Appl. Math.14, 599–617 (1961)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Whitney, H.: Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc.36, 63–89 (1934)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • S. Alinhac
    • 1
  • M. S. Baouendi
    • 2
  1. 1.Départment de MathématiquesUniversité de Paris-SudOrsay CedexFrance
  2. 2.Department of MathematicsUniversity of CaliforniaLa JollaUSA

Personalised recommendations