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Estimations L p de l’équation des ondes sur les variétés à singularité conique

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Résumé

Dans cet article, on se propose d’abord d’améliorer le résultat de (Trans. Amer. Math. Soc. 355:689–711, 2003). Plus précisement, soit N une variété riemannienne compacte de dimension n − 1 ≥ 2, sans bord, on montre que sur le cône C(N), l’opérateur des ondes, \({\frac{\sin{t \sqrt{-\Delta}}}{\sqrt{-\Delta}}}\), est borné sur L p(C(N)) avec la norme ≤ C p t pour \({|\frac{1}{p} - \frac{1}{2} | < \frac{1}{n-1}}\). Ensuite, on obtient les estimations L p des opérateurs \({(I - \Delta)^{-\gamma} e^{i t \sqrt{-\Delta}} (\gamma > 0, t > 0)}\) et apparentés.

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  1. School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai, 200433, People’s Republic of China

    Hong-Quan Li

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Li, HQ. Estimations L p de l’équation des ondes sur les variétés à singularité conique. Math. Z. 272, 551–575 (2012). https://doi.org/10.1007/s00209-011-0949-9

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