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

Hongjie Dong; Hong Zhang

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

Analysis of PDEs 2017-04-07 v2

Authors: Hongjie Dong , Hong Zhang

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.

Keywords

Schauder estimates nonlocal parabolic equations fully nonlinear equations rough kernels Zygmund space translation invariant

Cite

@article{arxiv.1604.00101,
  title  = {On Schauder estimates for a class of nonlocal fully nonlinear parabolic equations},
  author = {Hongjie Dong and Hong Zhang},
  journal= {arXiv preprint arXiv:1604.00101},
  year   = {2017}
}

Comments

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

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