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 \({\mathcal{S}(\mathbb{R})}\) and \({\mathcal{S}'(\mathbb{R})}\).
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Ascanelli, A., Cappiello, M. Weighted energy estimates for p-evolution equations in SG classes. J. Evol. Equ. 15, 583–607 (2015). https://doi.org/10.1007/s00028-015-0274-6
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DOI: https://doi.org/10.1007/s00028-015-0274-6