In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coefficients in any space dimension N ≥ 1. 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.

Time-Dependent Loss of Derivatives for Hyperbolic Operators with Non Regular Coefficients

DEL SANTO, DANIELE;
2013-01-01

Abstract

In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coefficients in any space dimension N ≥ 1. 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.
2013
http://www.tandfonline.com/doi/full/10.1080/03605302.2013.795968#.UbHgAuCaHyM
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2681746
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