Calculus of Variations and Partial Differential Equations

, Volume 49, Issue 1, pp 139–172

Regularity for solutions of non local parabolic equations


DOI: 10.1007/s00526-012-0576-2

Cite this article as:
Lara, H.C. & Dávila, G. Calc. Var. (2014) 49: 139. doi:10.1007/s00526-012-0576-2


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).

Mathematics Subject Classification (2000)


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA