董弘桀 教授学术报告
Title: Elliptic and parabolic equations with DMO coefficients
Speaker: Hongjie Dong (董弘桀)
Affiliation: Brown University, USA (美国布朗大学)
Time: 13:30 - 14:30, Wednesday, 8th January, 2025 （UTC+8, Beijing Time）
Venue: Room 1502, Shing-Tung Yau Center, Yifu Architecture Building, Sipailou Campus of Southeast University, Nanjing（东南大学四牌楼校区逸夫建筑馆丘成桐中心1502室）
Inviter: Feida Jiang（蒋飞达）
Abstract
I will present some recent results for elliptic and parabolic equations with Dini mean oscillation (DMO) coefficients. These are extensions of the classical Schauder estimates and the DMO continuity appears to be a minimal condition. For double divergence form equations, we obtained a Harnack inequality and higher regularity near nodel sets. As an application, we established a Hopf type lemma for double divergence form elliptic equations with DMO coefficients and a two-sided estimate for Green’s functions. Based on joint work with Seick Kim (Yonsei University), Luis Escauriaza (EHU), Jongkeun Choi (Pusan National University), and Boyan Sirakov (PUC-Rio).
Bio
Professor Hongjie Dong received his PhD from the University of Minnesota in 2005, under the supervision of Professor Nicolai Krylov. Prior to joining Brown University, he held positions at the University of Chicago and the Institute for Advanced Study in Princeton. He has been recognized with several prestigious grants and awards, including the NSF CAREER Award, a Simons Foundation Fellowship, and a Mid-Career Research Award from Brown University.