Browsing by Author "Fanelli, Francesco"

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    Time dependent loss of derivatives for hyperbolic operators with non-regular coefficients
    (2013-02-04) Colombini, Ferruccio; Del Santo, Daniele; Fanelli, Francesco; Metivier, Guy; Mathematics; Functional Analysis and Applications
    In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coe fficients in any space dimension N ≥ 1. We will suppose the coe fficients 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.