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math.AP2023
Sobolev spaces and trace theorems for time-fractional evolution equations
Doyoon Kim, Kwan Woo
We establish trace and extension theorems for evolutionary equations with the Caputo fractional derivatives in (weighted) spaces. To achieve this, we identify weighted Sobole…
math.AP2023
Time fractional parabolic equations with partially SMO coefficients
Hongjie Dong, Doyoon Kim
We present the unique solvability in Sobolev spaces of time fractional parabolic equations in divergence and non-divergence forms. The leading coefficients are merely measurable in…
math.AP2023
Green functions for stationary Stokes systems with conormal derivative boundary condition in two dimensions
Jongkeun Choi, Doyoon Kim
We construct Green functions of conormal derivative problems for the stationary Stokes system with measurable coefficients in a two dimensional Reifenberg flat domain.