威尼斯人

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 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 estimates for Green’s functions. Most part of my talk is based on joint work with Seick Kim (Yonsei University), Luis Escauriaza (EHU), Jongkeun Choi (Pusan National University), and Boyan Sirakov (PUC-Rio).

个人简介：董弘桀，美国布朗大学教授，博士生导师，师从著名数学家Nicolai V. Krylov。 目前从事偏微分方程等领域的研究，在 Comm. Pure Appl. Math., Arch.Rational Mech. Anal., Comm. Math. Phys., Adv. Math., JEMS等国际著名学术期刊上发表论文 140余篇，并担任 SIAM J. Math. Anal., J. Differential Equations 等期刊编委。