English

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

Analysis of PDEs 2013-09-19 v1

Abstract

In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coefficients in any space dimension N1N\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.

Keywords

Cite

@article{arxiv.1305.1095,
  title  = {Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients},
  author = {Ferruccio Colombini and Daniele Del Santo and Francesco Fanelli and Guy Métivier},
  journal= {arXiv preprint arXiv:1305.1095},
  year   = {2013}
}

Comments

to appear in Comm. Partial Differential Equations (2013)