Differential and Integral Equations

Sharp regularity of the coefficients in the Cauchy problem for a class of evolution equations

Massimo Cicognani and Ferruccio Colombini

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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.

Article information

Source
Differential Integral Equations, Volume 16, Number 11 (2003), 1321-1344.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060512

Mathematical Reviews number (MathSciNet)
MR2016685

Subjects
Primary: 35G10: Initial value problems for linear higher-order equations
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

Citation

Cicognani, Massimo; Colombini, Ferruccio. Sharp regularity of the coefficients in the Cauchy problem for a class of evolution equations. Differential Integral Equations 16 (2003), no. 11, 1321--1344. https://projecteuclid.org/euclid.die/1356060512


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