Sobolev spaces and trace theorems for time-fractional evolution equations

Doyoon Kim; Kwan Woo

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arXiv · 2307.03087

Sobolev spaces and trace theorems for time-fractional evolution equations

Doyoon Kim·Kwan Woo

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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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Doyoon Kim, Kwan Woo. 2023-07-06. Sobolev spaces and trace theorems for time-fractional evolution equations. https://arxiv.org/abs/2307.03087

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