We deal with the Cauchy problem for a $2$-evolution operator of Schr"odinger 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.
Cicognani M., Colombini F. (2004). Optimal Well-posedness of The Cauchy Problem for Evolution Equations with $C^{N}$ Coefficients. DIFFERENTIAL AND INTEGRAL EQUATIONS, 17, 1079-1092.
Optimal Well-posedness of The Cauchy Problem for Evolution Equations with $C^{N}$ Coefficients
CICOGNANI, MASSIMO;
2004
Abstract
We deal with the Cauchy problem for a $2$-evolution operator of Schr"odinger 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.File in questo prodotto:
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