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arXiv · 1305.1095

Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients

Ferruccio Colombini·Daniele Del Santo·Francesco Fanelli·Guy Métivier
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Abstract

In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coefficients in any space dimension $N\geq1$. 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.

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Ferruccio Colombini, Daniele Del Santo, Francesco Fanelli, Guy Métivier. 2013-05-06. Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients. https://doi.org/10.1080/03605302.2013.795968

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