Geodesic
Non-Lipschitz coefficients for strictly hyperbolic equations
Hirosawa, Fumihiko1 ; Reissig, Michael2 
1 Department of Mathematics Nippon Institute of Technology Saitama 345-8501, Japan
2 Fakultät für Mathematik und Informatik TU Bergakademie Freiberg 09596 Freiberg, Germany
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 3, pp. 589-608

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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 ∞ well posedness for weakly hyperbolic Cauchy problems or for strictly hyperbolic Cauchy problems with non-Lipschitz coefficients are optimal.

Classification : 35L15, 35L10, 35A05

Hirosawa, Fumihiko 1 ; Reissig, Michael 2

1 Department of Mathematics Nippon Institute of Technology Saitama 345-8501, Japan
2 Fakultät für Mathematik und Informatik TU Bergakademie Freiberg 09596 Freiberg, Germany 
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     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://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_3_589_0/}
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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://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_3_589_0/