Time-Dependent Loss of Derivatives for Hyperbolic Operators with Non Regular Coefficients
Time-Dependent Loss of Derivatives for Hyperbolic Operators with Non Regular Coefficients
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DOI：
10.1080/03605302.2013.795968
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发表时间：
2013-04
影响因子：
1.9
通讯作者：
F. Colombini;D. Santo;F. Fanelli;Guy M'etivier
中科院分区：
文献类型：
--
作者：
F. Colombini;D. Santo;F. Fanelli;Guy M'etivier
本文研究了在N ≥ 1的任意空间维中具有低正则系数的严格双曲型算子的Cauchy问题。我们将假设系数在时间上是log-Zygmund连续的，在空间上是log-Lipschitz连续的。带参数的准微分将是Sobolev空间中能量估计的主要工具，这些估计将呈现出依赖于时间的导数损失。
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.