On Schauder estimates for a class of nonlocal fully nonlinear parabolic equations

Abstract

We obtain Schauder estimates for a class of concave fully nonlinear nonlocal parabolic equations of order $σ\in (0,2)$ with rough and non-symmetric kernels. As a application, we prove that the solution to a translation invariant equation with merely bounded data is $C^σ$ in $x$ variable and $Λ^1$ in $t$ variable, where $Λ^1$ is the Zygmund space.

41 pages, added Remark 1.4 and the proof of Corollary 1.3. Accepted in CVPDE