Non unicité de Hölmgren pour des problèmes non linéaires

G. Métivier

Séminaire Équations aux dérivées partielles (Polytechnique) (1992-1993)

  • page 1-10

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Métivier, G.. "Non unicité de Hölmgren pour des problèmes non linéaires." Séminaire Équations aux dérivées partielles (Polytechnique) (1992-1993): 1-10. <http://eudml.org/doc/112050>.

@article{Métivier1992-1993,
author = {Métivier, G.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {Cauchy problem},
language = {fre},
pages = {1-10},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Non unicité de Hölmgren pour des problèmes non linéaires},
url = {http://eudml.org/doc/112050},
year = {1992-1993},
}

TY - JOUR
AU - Métivier, G.
TI - Non unicité de Hölmgren pour des problèmes non linéaires
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1992-1993
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 10
LA - fre
KW - Cauchy problem
UR - http://eudml.org/doc/112050
ER -

References

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  1. [A] S. Alinhac: Uniqueness and non-uniqueness in the Cauchy problem. Contemporary Mathematics, 27 (1894), pp 1-22. Zbl0574.35002MR741036
  2. [AB] S. Alinhac - S. Baouendi: Construction de solutions nulles et singulières pour des opérateurs de type principal. Séminaire de L'École Polytechnique, année 1978-79, exposé 22. Zbl0427.35082MR557533
  3. [AM] S. Alinhac, G. Métivier: propagation de l'analyticité des solutions d'équations nonlinéaires de type principal. Comm. in Partial Diff. Equ., 9 (1984) pp 523-537. Zbl0566.35017MR742507
  4. [BGT] S. Baouendi, C. Goulaouic, F.TREVES: Uniqueness in certain first order nonlinear complex Cauchy problems. Comm. in Pure and Applied Math., 38 (1985), pp 109-123. Zbl0609.35019MR768106
  5. [Ba] H. Bahouri: Non unicité du problème de Cauchy pour des opérateurs à symbole principal réel. Comm. in Partial Diff. Equ., 8 (1983), pp 1521-1547. Zbl0539.35002MR728872
  6. [Bo 1] J.M. Bony: Une extension du théorème de Hölmgren sur l'unicité du problème de Cauchy. C.R. Acad. Sci. Paris, 268 (1969) pp 1103-1106. Zbl0172.38001MR241805
  7. [Bo 2] J.M. Bony: Extensions du théorème de Hölmgren. Sém. Goulaouic-Schwartz, École Polytechnique, Année 1975-76. Zbl0336.35003MR474426
  8. [Co] P. Cohen: The non uniqueness of the Cauchy problem. O.N.R. Techn. Report93, Stanford1960. 
  9. [DG] E. De Giorgi: Un esempio di non unicita della soluzione del problema di Cauchy relativo ad una equazione differentiale lineare a derivati parziali di typo parabolico. Rend. Mat.14 (1955) pp 382-387. Zbl0064.34504MR70028
  10. [HT] N. Hanges, F. Treves: On the analyticity of solutions of first order nonlinear PDE. Trans. of the Amer. Math. Soc., 331 (1992), pp 627-638. Zbl0758.35018MR1061776
  11. [Höl] E. Hölmgren: Uber Systeme von linearen partialen Dif ferentialgleichtungen. Öfversigt af Kongl. Vetenskaps-Akad. Foh58 (1901), pp 91-105. JFM32.0357.02
  12. [Hör 1] L. Hörmander: Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients. Comm. on Pure and Appl. Math., 24 (1971) pp 671-704. Zbl0226.35019MR294849
  13. [Hör 1] L. Hörmander: A remark on Hölmgren's uniqueness theorem. J. Diff. Geom., 6 (1971), pp 129-134. Zbl0221.35002MR320486
  14. [Hör 3] L. Hörmander: The analysis of linear partial differential operators. Springer Verlag, Berlin (1983). 
  15. [J] F. John: On linear dif ferential equations with analytic coefficients. Unique continuation of data. Comm. on Pure and Appl. Math., 2 (1949) pp 209-253. Zbl0035.34601MR36930
  16. [M] G. Métivier: Uniqueness and approximation of solutions of first order non linear equations. Invent. Math., 82 (1985) pp 263-282. Zbl0594.35018MR809715
  17. [Mo] C.B. Morrey: On the analyticity of the solution s of analytic nonlinear systems of partial differential equations. Tech. Report No 8, Univ .of Calif., Berkeley (1957). Multiple integrals in the calculus of variations. Berin -Heidelberg-New York, Springer1966. 
  18. [Pe] I. Petrowski: Sur l'analyticité des solutions des systèmes d'équations différentielles. Ree. Math. N.S. Math Sbomick5 (1939), pp 3-70. MR1425JFM65.0405.02
  19. [Pl] A. Plis: The problem of uniqueness for the solution of a system of partial dif ferential equations. Bull. Acad. Pol. Sci.2 (1954) pp 55-57. Zbl0055.32304MR64279
  20. [Sa] M. Sato: Hyperfunctions and partial differential equations. Proc. Int. Conf. on Funct. Anal. and Rel. Topics., Tokyo University Press, Tokyo (1969), pp 91-94. Zbl0208.35801
  21. [SKK] M. Sato, T. Kawai, M. Kashiwara: Microfunctions and pseudodifferential equations. Springer Lectures Notes in Mathematics, 287 (1973). Zbl0277.46039MR420735
  22. [Sjö] J. Sjöstrand: Singularités analytiques microlocales. Astérisque95, (1982) pp 1- 166. Zbl0524.35007MR699623
  23. [T] F. Treves: Hypo-analytic structures. Princeton Univ. Press. (à paraître). Zbl0787.35003MR1200459
  24. [Z] C. Zuily: Uniqueness and non-uniqueness in the Cauchy problem. Progress in Math., vol 33, Birkhäuser, Boston (1983). Zbl0521.35003MR701544

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