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 well posedness for weakly hyperbolic Cauchy problems or for strictly hyperbolic Cauchy problems with non-Lipschitz coefficients are optimal.
@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},
mrnumber = {2099250},
zbl = {1170.35471},
language = {en},
url = {http://archive.numdam.org/item/ASNSP_2004_5_3_3_589_0/}
}
TY - JOUR AU - Hirosawa, Fumihiko AU - Reissig, Michael TI - Non-Lipschitz coefficients for strictly hyperbolic equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2004 SP - 589 EP - 608 VL - 3 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2004_5_3_3_589_0/ LA - en ID - ASNSP_2004_5_3_3_589_0 ER -
%0 Journal Article %A Hirosawa, Fumihiko %A Reissig, Michael %T Non-Lipschitz coefficients for strictly hyperbolic equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2004 %P 589-608 %V 3 %N 3 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2004_5_3_3_589_0/ %G en %F 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://archive.numdam.org/item/ASNSP_2004_5_3_3_589_0/
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