Weighted energy estimates for $p$-evolution equations

TL;DR

This paper establishes weighted energy estimates for linear p-evolution equations, ensuring well-posedness in Schwartz spaces by analyzing coefficient behavior at infinity.

Contribution

It introduces new weighted energy estimates for p-evolution equations under specific coefficient conditions, advancing the understanding of their well-posedness.

Findings

Energy estimates in weighted Sobolev spaces

Well-posedness in Schwartz spaces

Conditions on coefficients at infinity

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 $\mathcal{S}'$.