Regularity results for fully nonlinear parabolic integro-differential operators

2011/09/17 by Yong‐Cheol Kim, Yong-Cheol Kim, Kim, Yong-Cheol +2 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #math.AP #msc:35B65 #msc:35D10 #msc:35J60 #msc:45K05 #msc:47G20

paper · pdf · doi:10.48550/arxiv.1109.3807

arxiv created 2011/10/13 · arxiv updated 2011/10/14

Abstract

In this paper, we consider the regularity theory for fully nonlinear parabolic integro-differential equations with symmetric kernels. We are able to find parabolic versions of Alexandrov-Backelman-Pucci estimate with 0<σ<2. And we show a Harnack inequality, Hölder regularity, and C^1,α-regularity of the solutions by obtaining decay estimates of their level sets.

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• Cordes-Nirenberg type estimates for nonlocal parabolic equations

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