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FIELD Math:Analysis
DATE February 20 (Wed), 2019
TIME 16:00-17:30
PLACE 1423
SPEAKER Kim, Soojung
HOST Kang, Nam-Gyu
INSTITUTE  
TITLE Harnack inequality on Riemannian manifolds via the ABP method
ABSTRACT

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.

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