Autour du théorème de Holmgren sur l'unicité de Cauchy (Q2266812)

The author extends a unicity theorem of \textit{J.-M. Bony} [C. R. Acad. Sci. Paris, Sér. I, 268, 1103-1106 (1969; Zbl 0172.380)], the novelty of the proof resting on the computation of the Hausdorff dimension of the normal fiber bundle to a closed set. Then he establishes, for a complex principal symbol, the equivalent of the non-unicity theorem of \textit{E. C. Zachmanoglou} [Arch. Ration. Mech. Anal. 27, 373-384 (1968; Zbl 0159.385)]; however in the analytic case extra hypotheses are needed to obtain a solution with support in a half-space.