The overdetermined Cauchy problem
Annales de l'Institut Fourier, Tome 47 (1997) no. 1, pp. 155-199.

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.

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.

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Boiti, Chiara; Nacinovich, Mauro. The overdetermined Cauchy problem. Annales de l'Institut Fourier, Tome 47 (1997) no. 1, pp. 155-199. doi : 10.5802/aif.1564. http://www.numdam.org/articles/10.5802/aif.1564/

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