Non-Lipschitz coefficients for strictly hyperbolic equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 3, pp. 589-608.

In the present paper we explain the classification of oscillations and its relation to the loss of derivatives for a homogeneous hyperbolic operator of second order. In this way we answer the open question if the assumptions to get ${C}^{\infty }$ well posedness for weakly hyperbolic Cauchy problems or for strictly hyperbolic Cauchy problems with non-Lipschitz coefficients are optimal.

Classification : 35L15,  35L10,  35A05
@article{ASNSP_2004_5_3_3_589_0,
author = {Hirosawa, Fumihiko and Reissig, Michael},
title = {Non-Lipschitz coefficients for strictly hyperbolic equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {589--608},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 3},
number = {3},
year = {2004},
zbl = {1170.35471},
mrnumber = {2099250},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2004_5_3_3_589_0/}
}
Hirosawa, Fumihiko; Reissig, Michael. Non-Lipschitz coefficients for strictly hyperbolic equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 3, pp. 589-608. http://www.numdam.org/item/ASNSP_2004_5_3_3_589_0/

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