A well-posedness result for hyperbolic operators with Zygmund coefficients

被引：8

作者：

Colombini, Ferruccio ^{[1
]}

Del Santo, Daniele ^{[2
]}

Fanelli, Francesco ^{[3
]}

Metivier, Guy ^{[4
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy

[2] Univ Trieste, Dipartimento Matemat & Geosci, I-34127 Trieste, Italy

[3] Univ Paris Est, LAMA, UPEC, UPEMLV,CNRS,UMR 8050, F-94010 Creteil, France

[4] Univ Bordeaux 1, IMB, F-33405 Talence, France

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2013年 / 100卷 / 04期

关键词：

Strictly hyperbolic operators; Non-Lipschitz coefficients; Zygmund regularity; Energy estimates; H-infinity well-posedness; EQUATIONS;

D O I：

10.1016/j.matpur.2013.01.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove an energy estimate with no loss of derivatives for a strictly hyperbolic operator with Zygmund continuous second order coefficients both in time and in space. In particular, this estimate implies the well-posedness for the related Cauchy problem. On the one hand, this result is quite surprising, because it allows to consider coefficients which are not Lipschitz continuous in time. On the other hand, it holds true only in the very special case of initial data in H-1/2 x H-1/2. Paradifferential calculus with parameters is the main ingredient to the proof. (C) 2013 Elsevier Masson SAS. All rights reserved.

引用

页码：455 / 475

页数：21

共 17 条

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