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

  • Hongjie DongEmail author
  • Hong Zhang
Article
  • 27 Downloads

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. 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 Classification

Primary 35K55 Secondary 35B45 35B65 35R09 

Notes

Acknowledgements

The authors would like to thank the referees for their careful review as well as many valuable comments and suggestions.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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