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Article Dans Une Revue American Journal of Mathematics Année : 2006

Long-time existence for semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds

Résumé

We prove a long time existence result for semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds. This generalizes a preceding result concerning the case of spheres, obtained in [9]. The proof relies on almost orthogonality properties of products of eigenfunctions of positive elliptic selfadjoint operators on a compact manifold and on the specific distribution of eigenvalues of the laplacian perturbed by a potential on Zoll manifolds.
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Dates et versions

hal-00359308 , version 1 (06-02-2009)

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  • HAL Id : hal-00359308 , version 1

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Jean-Marc Delort, Jérémie Szeftel. Long-time existence for semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds. American Journal of Mathematics, 2006, 128, pp.1187-1218. ⟨hal-00359308⟩
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