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 C1 for a totally characteristic hypersurface (the Goursat problem).

Received: 2005-11-27
Accepted: 2007-03-06
Published online: 2007-05-04
DOI: 10.1016/j.crma.2007.03.010

@article{CRMATH_2007__344_10_621_0,
     author = {Jean-Philippe Nicolas},
     title = {On {Lars} {H\"ormander's} remark on the characteristic {Cauchy} problem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {621--626},
     publisher = {Elsevier},
     volume = {344},
     number = {10},
     year = {2007},
     doi = {10.1016/j.crma.2007.03.010},
     language = {en},
}

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Jean-Philippe Nicolas. On Lars Hörmander's remark on the characteristic Cauchy problem. Comptes Rendus. Mathématique, Volume 344 (2007) no. 10, pp. 621-626. doi : 10.1016/j.crma.2007.03.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.010/