Weighted energy estimates for $p$-evolution equations

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 $\mathcal{S}$ and ${\mathcal{S}}^{\prime }$.

18 pages

Cited by in corpus (1)

• A necessary condition for $H^{\infty }$ well-posedness of p-evolution equations