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.
Time-Dependent Loss of Derivatives for Hyperbolic Operators with Non Regular Coefficients / Colombini, F.; DEL SANTO, Daniele; Fanelli, F.; Métivier, G.. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 38:10(2013), pp. 1791-1817. [10.1080/03605302.2013.795968]
Time-Dependent Loss of Derivatives for Hyperbolic Operators with Non Regular Coefficients
DEL SANTO, DANIELE;
2013-01-01
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.Pubblicazioni consigliate
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