Calculus of Variations and Partial Differential Equations

, Volume 49, Issue 1, pp 139–172

Regularity for solutions of non local parabolic equations

Authors

  • Héctor Chang Lara
    • Department of MathematicsUniversity of Texas at Austin
    • Department of MathematicsUniversity of Texas at Austin
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
  • 579 Views

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)

35K5535B6535B4535D4035R09
Download to read the full article text

Copyright information

© Springer-Verlag Berlin Heidelberg 2012