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Time-Dependent Loss of Derivatives for Hyperbolic Operators with Non Regular Coefficients |
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| Authors: | Ferruccio Colombini Daniele Del Santo Guy Métivier |
| Institution: | 1. Dipartimento di Matematica , Università di Pisa , Pisa , Italy;2. Dipartimento di Matematica e Geoscienze , Università di Trieste , Trieste , Italy;3. Institut de Mathématiques de Bordeaux, UMR 5251 , Université de Bordeaux 1 , Talence , France |
| Abstract: | In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coefficients in any space dimension N ≥ 1. We will suppose the coefficients to be log-Zygmund continuous in time and log-Lipschitz continuous in space. Paradifferential calculus with parameters will be the main tool to get energy estimates in Sobolev spaces and these estimates will present a time-dependent loss of derivatives. |
| Keywords: | Energy estimates Hyperbolic operators Log-Zygmund regularity Non-Lipschitz coefficient Well-posedness |