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 $\sigma \in (0,2)$ with rough and non-symmetric kernels. As a application, we prove that the solution to a translation invariant equation with merely bounded data is $C^{\sigma }$ in $x$ variable and ${\Lambda }^1$ in $t$ variable, where ${\Lambda }^1$ is the Zygmund space.

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

References in corpus (1)

• $C^{\s+\a}$ estimates for concave, non-local parabolic equations with critical drift

Cited by in corpus (1)

• Dini estimates for nonlocal fully nonlinear elliptic equations