On Schauder estimates for a class of nonlocal fully nonlinear parabolic equations
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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. We also 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. From these results, we can derive the corresponding results for nonlocal elliptic equations with rough and non-symmetric kernels, which are new even in this case.
Mathematics Subject ClassificationPrimary 35K55 Secondary 35B45 35B65 35R09
The authors would like to thank the referees for their careful review as well as many valuable comments and suggestions.
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