|DATE||February 20 (Wed), 2019|
|TITLE||Harnack inequality on Riemannian manifolds via the ABP method|
We study the Harnack inequality of elliptic and parabolic equations in nondivergence form. The Aleksandrov-Bakelman-Pucci (ABP for short) estimate plays a crucial role in the proof of the Krylov-Safonov Harnack inequality for nondivergent equations with bounded measurable coefficients. The Krylov-Safonov theory is the analogue of the De Giorgi-Nash-Moser theory for divergent equations. In this talk, we discuss the ABP estimate and the Harnack inequality for nonlinear elliptic and parabolic equations on Riemannian manifolds with Ricci curvature bounded from below.