Regularity for solutions of non local parabolic equations

Details Regularity for solutions of non local parabolic equations Regularity for solutions of non local parabolic equations

2011-09-15

arxiv.org/abs/1109.3247v1

Mathematics

Analysis of PDEs

Scientific paper

We study the regularity of solutions of parabolic fully nonlinear nonlocal equations. We proof $C^\a$ regularity in space and time and for translation invariant equations and under different assumptions on the kernels $C^{1,\a}$ in space and time regularity. The proofs rely on a weak parabolic ABP inspired in recent work done by L. Silvestre and the classic ideas of K. Tso and L. Wang. Our results remain uniform as $\s\to2$ allowing us to understand the non local theory as an extension to the classical one.

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