Regularity for solutions of non local parabolic equations. (English) Zbl 1292.35068
The authors show the regularity of solutions of parabolic fully nonlinear nonlocal equations. Their results are natural extension of Krylov-Safonov techniques. The main results of this paper are proofs of the Hölder regularity (in space and time) for the solutions and, only in space, for the gradient of the solutions for translation-invariant equations. The proofs are based on a weak parabolic version of the Aleksandrov-Bakelman-Pucci-Krylov-Tso theorem. The authors extend the techniques introduced by Tso getting stable estimates when the singularity of the kernel tends to \(n +2\). This stability result is new and very interesting.
Reviewer: Vincenzo Vespri (Firenze)
MSC:
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35K55 | Nonlinear parabolic equations |
| 35B45 | A priori estimates in context of PDEs |
| 35D40 | Viscosity solutions to PDEs |
| 35R09 | Integro-partial differential equations |
Keywords:
non-divergence case; Harnack estimates; fully nonlinear equations; Hölder regularity; Aleksandrov-Bakelman-Pucci-Krylov-Tso theoremReferences:
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