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세미나

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NUMBER  
AUTHOR Lee, Ki-Ahm
TITLE Harnack inequality for nonlocal operators on manifolds with nonnegative curvature
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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.
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