Sobolev spaces and trace theorems for time-fractional evolution equations

2023/07/06 by Kim, Doyoon, Woo, Kwan
#35B30 #35B65 #35K15 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.03087

Abstract

We establish trace and extension theorems for evolutionary equations with the Caputo fractional derivatives in (weighted) L_p spaces. To achieve this, we identify weighted Sobolev and Besov spaces with mixed norms that accommodate solution spaces and their initial values well-suited for equations involving time-fractional derivatives. Our analysis encompasses both time-fractional sub-diffusion and super-diffusion equations. We also provide observations on the initial behavior of solutions to time-fractional equations.

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