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We prove that the Cauchy problem for a class of hyperbolic equations with non-Lipschitz coefficients is well-posed in and in Gevrey spaces. Some counter examples are given showing the sharpness of these results.
@article{ASNSP_2002_5_1_2_327_0,
author = {Colombini, Ferruccio and del Santo, Daniele and Kinoshita, Tamotu},
title = {Well-posedness of the {Cauchy} problem for a hyperbolic equation with {non-Lipschitz} coefficients},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {327--358},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 1},
number = {2},
year = {2002},
mrnumber = {1991143},
zbl = {1098.35094},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_2_327_0/}
}
TY - JOUR AU - Colombini, Ferruccio AU - del Santo, Daniele AU - Kinoshita, Tamotu TI - Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2002 SP - 327 EP - 358 VL - 1 IS - 2 PB - Scuola normale superiore UR - http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_2_327_0/ LA - en ID - ASNSP_2002_5_1_2_327_0 ER -
%0 Journal Article %A Colombini, Ferruccio %A del Santo, Daniele %A Kinoshita, Tamotu %T Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2002 %P 327-358 %V 1 %N 2 %I Scuola normale superiore %U http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_2_327_0/ %G en %F ASNSP_2002_5_1_2_327_0
Colombini, Ferruccio; del Santo, Daniele; Kinoshita, Tamotu. Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 2, pp. 327-358. http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_2_327_0/