## Differential and Integral Equations

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

#### 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