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arXiv · 2101.06903

Harnack inequality for Nonlocal operators on Manifolds with nonnegative curvature

Jongmyeong Kim·Minhyun Kim·Ki-Ahm Lee
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Abstract

We establish the Krylov Safonov Harnack inequalities and Holder estimates for fully nonlinear nonlocal operators of non-divergence form on Riemannian manifolds with nonnegative sectional curvatures. To this end, we first define the nonlocal Pucci operators on manifolds that give rise to the concept of non-divergence form operators. We then provide the uniform regularity results for these operators which recover the classical results for second order local operators as limits.

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Jongmyeong Kim, Minhyun Kim, Ki-Ahm Lee. 2021-01-18. Harnack inequality for Nonlocal operators on Manifolds with nonnegative curvature. https://doi.org/10.1007/s00526-021-02124-0

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