Regularity for solutions of non local parabolic equations

Article

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

Abstract

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)

35K55 35B65 35B45 35D40 35R09 

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA