| AUTHOR |
Lee, Ki-Ahm |
| TITLE |
Harnack inequality for nonlocal operators on manifolds with nonnegative curvature |
| ARCHIVE |
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| FILE |
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| JOURNAL |
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2022 |
| 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 estimates for these operators which recover the classical estimates for second order local operators as limits. |
