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2003 Sharp regularity of the coefficients in the Cauchy problem for a class of evolution equations
Massimo Cicognani, Ferruccio Colombini
Differential Integral Equations 16(11): 1321-1344 (2003).

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 a $p$-evolution operator of Schrödinger type. We use and mix two different scales of regularity of global and local type: the modulus of Hölder continuity and/or the behavior with respect to $|t-t_0|^{-q},\ q\geq 1,$ of the first derivative as $t$ tends to a point $t_0$. Both are ways to weaken the Lipschitz regularity. We give also counterexamples to show that the conditions we find are sharp.

Citation

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Massimo Cicognani. Ferruccio Colombini. "Sharp regularity of the coefficients in the Cauchy problem for a class of evolution equations." Differential Integral Equations 16 (11) 1321 - 1344, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

MathSciNet: MR2016685

Subjects:
Primary: 35G10
Secondary: 35B30

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 11 • 2003
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