The overdetermined Cauchy problem
Annales de l'Institut Fourier, Volume 47 (1997) no. 1, p. 155-199
We consider the (characteristic and non-characteristic) Cauchy problem for a system of constant coefficients partial differential equations with initial data on an affine subspace of arbitrary codimension. We show that evolution is equivalent to the validity of a principle on the complex characteristic variety and we study the relationship of this condition with the one introduced by Hörmander in the case of scalar operators and initial data on a hypersurface.
On considère le problème de Cauchy (caractéristique et non-caractéristique) pour les systèmes d’équations aux dérivées partielles à coefficients constants et données initiales sur un sous-espace affine de codimension arbitraire. On montre que l’évolution est équivalente à la validité d’un principe de Phragmén-Lindelöf sur la variété caractéristique complexe et on étudie ensuite la relation avec les conditions formulées par Hörmander dans le cas d’un opérateur scalaire et données sur une hypersurface.
@article{AIF_1997__47_1_155_0,
     author = {Boiti, Chiara and Nacinovich, Mauro},
     title = {The overdetermined Cauchy problem},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {47},
     number = {1},
     year = {1997},
     pages = {155-199},
     doi = {10.5802/aif.1564},
     zbl = {0865.35091},
     mrnumber = {98a:35095},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1997__47_1_155_0}
}
Boiti, Chiara; Nacinovich, Mauro. The overdetermined Cauchy problem. Annales de l'Institut Fourier, Volume 47 (1997) no. 1, pp. 155-199. doi : 10.5802/aif.1564. http://www.numdam.org/item/AIF_1997__47_1_155_0/

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