Regularity for solutions of non local parabolic equations

Calculus of Variations and Partial Differential Equations volume 49, pages 139–172 (2014)Cite this article

Abstract

We study the regularity of solutions of parabolic fully nonlinear nonlocal equations. We prove C α regularity in space and time and, under different assumptions on the kernels, C 1,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).

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  1. Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, TX, 78712, USA

    Héctor Chang Lara & Gonzalo Dávila

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  1. Héctor Chang Lara
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  2. Gonzalo Dávila
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Correspondence to Gonzalo Dávila.

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Communicated by O.Savin.

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Lara, H.C., Dávila, G. Regularity for solutions of non local parabolic equations. Calc. Var. 49, 139–172 (2014). https://doi.org/10.1007/s00526-012-0576-2

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Mathematics Subject Classification (2000)

  • 35K55
  • 35B65
  • 35B45
  • 35D40
  • 35R09