Time dependent loss of derivatives for hyperbolic operators with non-regular coefficients
Abstract
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.
Domains
Analysis of PDEs [math.AP]
Origin : Files produced by the author(s)
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