## Differential and Integral Equations

### Optimal well-posedness of the Cauchy problem for evolution equations with $C^N$ coefficients

#### Abstract

We deal with the Cauchy problem for a $2$-evolution operator of Schrödinger type with $C^N$ coefficients in the time variable, $N>2$. We find the Levi conditions for well-posedness in Gevrey classes of index $1/2 + N/4$, which is the best possible, as we show by means of counterexamples.

#### Article information

Source
Differential Integral Equations, Volume 17, Number 9-10 (2004), 1079-1092.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060314

Mathematical Reviews number (MathSciNet)
MR2082460

Zentralblatt MATH identifier
1150.35351

#### Citation

Cicognani, Massimo; Colombini, Ferruccio. Optimal well-posedness of the Cauchy problem for evolution equations with $C^N$ coefficients. Differential Integral Equations 17 (2004), no. 9-10, 1079--1092. https://projecteuclid.org/euclid.die/1356060314