%0 Journal Article
%T Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients
%A Ferruccio Colombini
%A Daniele Del Santo
%A Francesco Fanelli
%A Guy M¨¦tivier
%J Mathematics
%D 2013
%I arXiv
%R 10.1080/03605302.2013.795968
%X 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.
%U http://arxiv.org/abs/1305.1095v1