Harnack inequality for nonlocal operators on manifolds with nonnegative curvature
Abstract We establish the Krylov–Safonov Harnack inequalities and Hölder 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.
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.
Abstract
We establish the Krylov–Safonov Harnack inequalities and Hölder 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.
Springer
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