On lars Hörmander’s remark on the characteristic Cauchy problem. (English) Zbl 1124.35037

The author re-considers a result of L. Hörmander [J. Funct. Anal. 93, No. 2, 270–277 (1990; Zbl 0724.35060)], concerning a characteristic Cauchy problem for a class of wave equations on spatially compact space-times, with initial data on hypersurfaces that were weakly spacelike. The metric on the space-time and the first-order perturbation were assumed to be smooth. Here the author extends the result to a Lipschitz metric \(g^{jk}\), namely for the equation \(\partial^2_t u- g^{jk}\partial_j\partial_k u= 0\), with Einstein notation.


35L15 Initial value problems for second-order hyperbolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35L05 Wave equation


Zbl 0724.35060
Full Text: DOI arXiv Numdam EuDML


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