We study p-evolution equations of order m greater than 2 with coefficients depending both on t and x, not regular with respect to the time variable. We find the sharp regularity in time for the coefficients in order to have well posedness in H^1 of the related Cauchy Problem. We consider the case of continuous in time coefficients having the first time-derivative that breaks down at a point t_0, say t_0 = 0. The case m = 2 has already been studied by Cicognani and Colombini; here we generalize the result to operators of higher order.
The Cauchy Problem for a Class of p-evolution Equations
ASCANELLI, Alessia
2004
Abstract
We study p-evolution equations of order m greater than 2 with coefficients depending both on t and x, not regular with respect to the time variable. We find the sharp regularity in time for the coefficients in order to have well posedness in H^1 of the related Cauchy Problem. We consider the case of continuous in time coefficients having the first time-derivative that breaks down at a point t_0, say t_0 = 0. The case m = 2 has already been studied by Cicognani and Colombini; here we generalize the result to operators of higher order.File in questo prodotto:
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