Regularity for solutions of non local parabolic equations
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- Lara, H.C. & Dávila, G. Calc. Var. (2014) 49: 139. doi:10.1007/s00526-012-0576-2
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We study the regularity of solutions of parabolic fully nonlinear nonlocal equations. We prove Cα regularity in space and time and, under different assumptions on the kernels, C1,α in space for translation invariant equations. The proofs rely on a weak parabolic ABP and the classic ideas of Tso (Commun. Partial Diff. Equ. 10(5):543–553, 1985) and Wang (Commun. Pure Appl. Math. 45(1), 27–76, 1992). Our results remain uniform as σ → 2 allowing us to recover most of the regularity results found in Tso (Commun. Partial Diff. Equ. 10(5):543–553, 1985).