Weighted energy estimates for p-evolution equations

2013/09/24 by Alessia Ascanelli, Marco Cappiello, Ascanelli, Alessia +1
Engineering · Mathematics · #35G10 #35S05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #advanced mathematical theories #math.AP #msc:35G10 #msc:35S05

paper · pdf · doi:10.48550/arxiv.1309.6102

18 pages

arxiv created 2013/09/24 · openalex publication_date 2013/09/24 · arxiv updated 2013/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 S and S'.

Related

• Linear and quasilinear evolution equations in the context of weighted L_p-spaces
• Linear and quasilinear evolution equations in the context of weighted L_p-spaces
• Pitt inequality for the linear structurally damped σ-evolution equations
• On weighted mixed-norm Sobolev estimates for some basic parabolic equations
• A regularity theory for evolution equations with time-measurable pseudo-differential operators in weighted mixed-norm Sobolev-Lipschitz spaces