A remark on Hörmander’s uniqueness theorem
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- by D. Del Santo and X. Saint Raymond PDF
- Proc. Amer. Math. Soc. 117 (1993), 721-725 Request permission
Abstract:
By using the paradifferential calculus, Hörmander’s classical uniqueness theorem for the Cauchy problem is shown to hold for operators with ${\mathcal {C}^2}$ coefficients in the principal part, instead of ${\mathcal {C}^\infty }$, under a special normality assumption.References
- S. Alinhac, Uniqueness and nonuniqueness in the Cauchy problem, Microlocal analysis (Boulder, Colo., 1983) Contemp. Math., vol. 27, Amer. Math. Soc., Providence, RI, 1984, pp. 1–22. MR 741036, DOI 10.1090/conm/027/741036
- Jean-Michel Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sci. École Norm. Sup. (4) 14 (1981), no. 2, 209–246 (French). MR 631751, DOI 10.24033/asens.1404
- P. Gérard and J. Rauch, Propagation de la régularité locale de solutions d’équations hyperboliques non linéaires, Ann. Inst. Fourier (Grenoble) 37 (1987), no. 3, 65–84 (French, with English summary). MR 916274, DOI 10.5802/aif.1098 L. Hörmander, Linear partial differential operators, Springer-Verlag, Berlin, 1963. —, The analysis of linear partial differential operators, vol. IV, Springer-Verlag, Berlin, 1985.
- Guy Métivier, Interaction de deux chocs pour un système de deux lois de conservation, en dimension deux d’espace, Trans. Amer. Math. Soc. 296 (1986), no. 2, 431–479 (French, with English summary). MR 846593, DOI 10.1090/S0002-9947-1986-0846593-9
- Claude Zuily, Uniqueness and nonuniqueness in the Cauchy problem, Progress in Mathematics, vol. 33, Birkhäuser Boston, Inc., Boston, MA, 1983. MR 701544, DOI 10.1007/978-1-4899-6656-8
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 721-725
- MSC: Primary 35L30; Secondary 35A07, 35S50
- DOI: https://doi.org/10.1090/S0002-9939-1993-1145944-7
- MathSciNet review: 1145944