On the uniqueness of the Cauchy problem for partial differential operators with multiple characteristics

Marvin Zeman

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1980)

  • Volume: 7, Issue: 2, page 257-285
  • ISSN: 0391-173X

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Zeman, Marvin. "On the uniqueness of the Cauchy problem for partial differential operators with multiple characteristics." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.2 (1980): 257-285. <http://eudml.org/doc/83838>.

@article{Zeman1980,
author = {Zeman, Marvin},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Cauchy problem; multiple characteristics; sub-principal symbol},
language = {eng},
number = {2},
pages = {257-285},
publisher = {Scuola normale superiore},
title = {On the uniqueness of the Cauchy problem for partial differential operators with multiple characteristics},
url = {http://eudml.org/doc/83838},
volume = {7},
year = {1980},
}

TY - JOUR
AU - Zeman, Marvin
TI - On the uniqueness of the Cauchy problem for partial differential operators with multiple characteristics
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1980
PB - Scuola normale superiore
VL - 7
IS - 2
SP - 257
EP - 285
LA - eng
KW - Cauchy problem; multiple characteristics; sub-principal symbol
UR - http://eudml.org/doc/83838
ER -

References

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  1. [1] A.P. Calderón, Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math., 80 (1958), pp. 16-36. Zbl0080.30302MR104925
  2. [2] A.P. Calderón, Existence and uniqueness theorems for systems of partial differential equations, in Fluid Dynamics and Applied Mathematics, Gordon and Breach, New York, 1962, pp. 147-195. Zbl0147.08202MR156078
  3. [3] T. Carleman, Sur un problème d'unicité pour les systèmes d'équations aux derivées partielles à deux variables indépendantes, Ark. Mat. Astr. Fys., 26B, no. 17 (1939), pp. 1-9. Zbl0022.34201JFM65.0394.03
  4. [4] P. Cohen, The non-uniqueness of the Cauchy problem, O.N.R. Tech. Rep. 93, Stanford, 1960. 
  5. [5] P.M. Goorjian, The uniqueness of the Cauchy problem for partial differential equations which may have multiple characteristics, Trans. Amer. Math. Soc., 146 (1969), pp. 493-509. Zbl0188.41502MR252832
  6. [6] L. Hörmander, On the uniqueness of the Cauchy problem I-II, Math. Scand.6 (1958), pp. 213-225; 7 (1959), pp. 177-190. Zbl0088.30201MR104924
  7. [7] L. Hörmander, Linear Partial Differential Operators, Springer-Verlag, Berlin-Göttingen- Heidelberg, 1964. Zbl0108.09301MR404822
  8. [8] L. Hörmander, Non-uniqueness for the Cauchy problem, in Fourier Integral Operators and Partial Differential Equations, Lecture Notes in Mathematics, Springer-Verlag, Berlin-Heidelberg-New York, 1975. Zbl0315.35019MR419980
  9. [9] J.J. Kohn - L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math., 18 (1965), pp. 269-305. Zbl0171.35101MR176362
  10. [10] W. Matsumoto, Uniqueness in the Cauchy problem for partial differential equations with multiple characteristic roots, J. Math. Kyoto Univ., 15, no. 3 (1975), pp. 479-525. Zbl0331.35014MR486945
  11. [11] S. Mizohata, Unicité du prolongement des solutions des équations elliptiques du quatrième ordre, Proc. Japan Acad., 34 (1958), pp. 687-692. Zbl0085.08501MR105553
  12. [12] S. Mizohata - Y. Ohya, Sur la condition de E. E. Levi concernant des équations hyperboliques, Publ. Res. Inst. Math. Sci., Kyoto Univ. Ser. A, 4 (1968), pp. 511-526. Zbl0202.37401MR276606
  13. [13] S. Mizohata - Y. Ohya, Sur la condition d'hyperbolicité pour les équations caractéristiques multiples, II, Japan. J. Math., 40 (1971), pp. 63-104. Zbl0231.35048MR303100
  14. [14] L. Nirenberg, Lectures on Partial Differential Equations, Proc. Reg. Conf. at Texas Tech., May 1972, Conf. Board of the A.M.S. 
  15. [15] Y. Ohya, On E. E. Levi's functions for hyperbolic equations with triple characteristics, Comm. Pure Appl. Math., 25 (1972), pp. 257-263. Zbl0238.35050MR298223
  16. [16] R.N. Pedersen, Uniqueness in Cauchy's problem for elliptic equations with double characteristics, Ark. Mat., 6 (1967), pp. 535-548. Zbl0146.34201
  17. [17] A. Plís, A smooth linear elliptic differential equation without any solution in a sphere, Comm. Pure Appl. Math., 14 (1961), pp. 599-617. Zbl0163.13103MR136846
  18. [18] M. Sussman, On uniqueness in Cauchy's problem for elliptic operators with characteristics of multiplicity greater than two, Tôhoku Math. J., 29 (1977), pp. 165-188. Zbl0355.35028MR463692
  19. [19] F. Tréves, Linear Partial Differential Equations with Constant Coefficients, Gordon and Breach, New York, 1966. Zbl0164.40602MR224958
  20. [20] K. Watanabe, On the uniqueness of the Cauchy problem for certain elliptic equations with triple characteristics, Tôhoku Math. J., 23 (1971), pp. 473-490. Zbl0237.35032MR308584
  21. [21] K. Watanabe - C. Zuily, On the uniqueness of the Cauchy problem for elliptic differential operators with smooth characteristics of variable multiplicity, Comm. Partial Differential Equations, 2, no. 8 (1977), pp. 831-854. Zbl0378.35023MR447800
  22. [22] M. Zeman, Uniqueness of solutions of the Cauchy problem for linear partial differential equations with characteristics of constant multiplicity, J. Differential Equations, 24 (1977), pp. 178-196. Zbl0349.35012MR599595
  23. [23] M. Zeman, Uniqueness of solutions of the Cauchy problem for linear partial differential equations with characteristics of variable multiplicity, J. Differential Equations, 27 (1978), pp. 1-18. Zbl0367.35055MR473447

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