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.

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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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. https://www.numdam.org/item/ASNSP_2004_5_3_3_589_0/

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