About the optimality of oscillations in non-Lipschitz coefficients for strictly hyperbolic equations

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Annali della Scuola Normale Superiore di Pisa- Classe di Scienze 3 (3):589-608 (2004)
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Abstract

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

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10.2422/2036-2145.2004.3.05

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