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

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.