We prove energy estimates for linear $p$-evolution equations in weighted Sobolev spaces under suitable assumptions on the behavior at infinity of the coefficients with respect to the space variables. As a consequence we obtain well posedness for the related Cauchy problem in the Schwartz spaces $\mathcal{S}(\R)$ and $\mathcal{S}'(\R)$.
Weighted energy estimates for p-evolution equations in SG classes
CAPPIELLO, Marco
2015-01-01
Abstract
We prove energy estimates for linear $p$-evolution equations in weighted Sobolev spaces under suitable assumptions on the behavior at infinity of the coefficients with respect to the space variables. As a consequence we obtain well posedness for the related Cauchy problem in the Schwartz spaces $\mathcal{S}(\R)$ and $\mathcal{S}'(\R)$.
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