We study the Cauchy problem for a class of $p$-evolution operators $P(t,x,D_t,D_x)$ in $[0,T]times {bf R}^n$, $p>1$, with less than ${mathcal C}^1$ coefficients with respect to the time variable. According to Lipschitz, Log-Lipschitz or H"older regularity we find well posedness in Sobolev spaces or in Gevrey classes.
Cicognani, M., Agliardi, R. (2004). Operators of $p$-evolution with non regular coefficients in the time variable. JOURNAL OF DIFFERENTIAL EQUATIONS, 202, 143-157 [10.1016/j.jde.2004.03.028].
Operators of $p$-evolution with non regular coefficients in the time variable
CICOGNANI, MASSIMO;AGLIARDI, ROSSELLA
2004
Abstract
We study the Cauchy problem for a class of $p$-evolution operators $P(t,x,D_t,D_x)$ in $[0,T]times {bf R}^n$, $p>1$, with less than ${mathcal C}^1$ coefficients with respect to the time variable. According to Lipschitz, Log-Lipschitz or H"older regularity we find well posedness in Sobolev spaces or in Gevrey classes.File in questo prodotto:
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