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Une Condition Suffisante Pour Que le Problème de Cauchy Soit Bien Posé

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Résumé

On prouve ici une estimation d’énergie pour le problème de Cauchy pour des opérateurs hyperboliques à caractéristiques au plus doubles qui contient à la fois les cas non effectivement hyperboliques voir L. Hörmander [3] et les cas effectivement hyperboliques, voir R. Melrose [8].

Abstract

We prove here an energy estimate for the Cauchy problem for hyperbolic equations with double characteristic, which contains both effectively and non-effectively points (see L. Hörmander [3] and R. Melrose [8]) in a unique framework.

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Références

  1. G. Eskin, Lectures on Linear Partial Differential Equation, Graduate Studies in Mathematics, American Mathematical Society, Vol. 123, 2011.

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Author information

Authors and Affiliations

  1. Institut de Mathèmatiques, Analyse Algébrique, Tour 15-25 5, Université Pierre et Marie Curie, 2 Place Jussieu, 75005, Paris, France

    Bernard Lascar

  2. Institut Mathématique de Jussieu, Analyse Algébrique Tour 15-25 4, 2 Place Jussieu, 75005, Paris, France

    Richard Lascar

Authors
  1. Bernard Lascar
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  2. Richard Lascar
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Correspondence to Richard Lascar.

Additional information

Dedicated to the memory of Prof. L. Boutet de Monvel

Bernard Lascar passed away on January 2012

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Lascar, B., Lascar, R. Une Condition Suffisante Pour Que le Problème de Cauchy Soit Bien Posé. Isr. J. Math. 211, 1–12 (2016). https://doi.org/10.1007/s11856-015-1269-2

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  • DOI: https://doi.org/10.1007/s11856-015-1269-2

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