Sobolev Spaces and Trace Theorems for Time-fractional Evolution Equations

초록

We establish trace and extension theorems for evolutionary equations with the Caputo fractional derivatives in (weighted) Lp$L_p$ 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.

키워드