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

Ferruccio Colombini (1) , Daniele del Santo (2) , Francesco Fanelli (3) , Guy Metivier (4)

1 Dipartimento di Matematica [Pisa]
2 Università degli studi di Trieste = University of Trieste
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
4 IMB - Institut de Mathématiques de Bordeaux

In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coe cients in any space dimension N>=1. We will suppose the coe cients to be log-Zygmund continuous in time and log-Lipschitz continuous in space. Paradi erential 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.

Domaines: Equations aux dérivées partielles [math.AP]

Ferruccio Colombini, Daniele del Santo, Francesco Fanelli, Guy Metivier. Time dependent loss of derivatives for hyperbolic operators with non-regular coefficients. 2012. ⟨hal-00733563⟩