Abstract
In 1990, L. Hörmander solved the Cauchy problem for the wave equation on a smooth spatially compact space–time, for data fixed on a Lipschitz and weakly spacelike hypersurface. He concluded his paper by a remark to the effect that his theorems should be valid for a Lipschitz metric. We extend his results to a Lipschitz metric for a spacelike hypersurface and to a metric whose regularity is intermediate between Lipschitz and C 1 for a totally characteristic hypersurface (the Goursat problem). To cite this article: J.-P. Nicolas, C. R. Acad. Sci. Paris, Ser. I 344 (2007).
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