Some uniqueness results for degenerate elliptic operators in two variables

Ferruccio Colombini; Daniele Del Santo

Rendiconti del Seminario Matematico della Università di Padova (1991)

  • Volume: 86, page 111-129
  • ISSN: 0041-8994

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Colombini, Ferruccio, and Del Santo, Daniele. "Some uniqueness results for degenerate elliptic operators in two variables." Rendiconti del Seminario Matematico della Università di Padova 86 (1991): 111-129. <http://eudml.org/doc/108227>.

@article{Colombini1991,
author = {Colombini, Ferruccio, Del Santo, Daniele},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {degenerate second order elliptic operator; unique continuation; Carleman estimates},
language = {eng},
pages = {111-129},
publisher = {Seminario Matematico of the University of Padua},
title = {Some uniqueness results for degenerate elliptic operators in two variables},
url = {http://eudml.org/doc/108227},
volume = {86},
year = {1991},
}

TY - JOUR
AU - Colombini, Ferruccio
AU - Del Santo, Daniele
TI - Some uniqueness results for degenerate elliptic operators in two variables
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1991
PB - Seminario Matematico of the University of Padua
VL - 86
SP - 111
EP - 129
LA - eng
KW - degenerate second order elliptic operator; unique continuation; Carleman estimates
UR - http://eudml.org/doc/108227
ER -

References

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  1. [1] S. Alinhac, Unicité du problème de Cauchy pour des opérateurs du second ordre d symboles réels, Ann. Inst. Fourier, Grenoble, 34 (1984), pp. 89-109. Zbl0507.35001MR746497
  2. [2] S. Alinhac - C. ZUILY, Unicité et non unicité du problème de Cauchy pour des opérateurs hyperboliques d caractéristiques doubles, Comm. in P. D. E., 7 (1981), pp. 799-828. Zbl0482.35052MR623646
  3. [3] M.S. Baouendi - E. C. ZACHMANOGLOU, Unique continuation of solutions of partial differential equations and inequalities from manifolds of any dimension, Duke Math. J., 45 (1978), pp. 1-13. Zbl0373.35001MR486484
  4. [4] A.P. Calderón, Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math., 80 (1958), pp. 16-36. Zbl0080.30302MR104925
  5. [5] P. Cohen, The non-uniqueness of the Cauchy problem, O.N.R. Techn. Report, 93, Stanford (1960). 
  6. [6] F. Colombini - D. Del Santo - C. Zuily, Uniqueness and non-uniqueness in the Cauchy problem of degenerate elliptic operators, to appear. Zbl0792.35065
  7. [7] F. Colombini - S. Spagnolo, A non-uniqueness result for the operators with principal part ∂2t + a(t) ∂2x,, in Partial Differential Equations and the Calculus of Variations Essays in honor de Ennio De Giorgi, Progress in Non-linear P.D.E. and their appl., vol. 1, Birkhäuser, Boston (1989), pp. 331-353. Zbl0694.35030
  8. [8] L. Nirenberg, Uniqueness in the Cauchy problem for a degenerate elliptic second order equation, in Differential Geometry and Complex Analysis, Springer-Verlag, Berlin (1985), pp. 213-218. Zbl0572.35043MR780047
  9. [9] X. Saint Raymond, L'unicité pour les problèmes de Cauchy linéaires du premier ordre, L'Ens. Math., 32 (1986), pp. 1-55. Zbl0625.35009MR850550
  10. [10] K. Watanabe, L'unicité du prolongement des solutions des équations elliptiques dégénérées, Tohoku Math. J., 34 (1982), pp. 239-249. Zbl0476.35016MR664731
  11. [11] C. Zuily, Uniqueness and non-uniqueness in the Cauchy problem, Progress in Math., Vol. 33, Birkhäuser, Boston (1983). Zbl0521.35003

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