We are concerned with the problem of determining the sharp regularity of the coefficients with respect to the time variable $t$ in order to have a well posed Cauchy problem in $H^infty$ or in Gevrey classes for linear or quasilinear hyperbolic operators of higher order. We use and mix two different scales of regularity of global and local type: the modulus of H"older continuity and/or the behaviour with respect to $|t-t_1|^{-q}, qgeq 1,$ of the first derivative as $t$ tends to a point $t_1$. Both are ways to weaken the Lipschitz regularity.

Coefficients with unbounded derivatives in hyperbolic equations

CICOGNANI, MASSIMO
2004

Abstract

We are concerned with the problem of determining the sharp regularity of the coefficients with respect to the time variable $t$ in order to have a well posed Cauchy problem in $H^infty$ or in Gevrey classes for linear or quasilinear hyperbolic operators of higher order. We use and mix two different scales of regularity of global and local type: the modulus of H"older continuity and/or the behaviour with respect to $|t-t_1|^{-q}, qgeq 1,$ of the first derivative as $t$ tends to a point $t_1$. Both are ways to weaken the Lipschitz regularity.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/4578
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