Harnack inequality for Nonlocal operators on Manifolds with nonnegative curvature
Analysis of PDEs
2021-01-19 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.2101.06903,
title = {Harnack inequality for Nonlocal operators on Manifolds with nonnegative curvature},
author = {Jongmyeong Kim and Minhyun Kim and Ki-Ahm Lee},
journal= {arXiv preprint arXiv:2101.06903},
year = {2021}
}