CAM Colloquium: Seick Kim (Yonsei University) - On Green's functions of nondivergent elliptic operators with continuous coefficients

Location

Frank H. T. Rhodes Hall 655

Description

Abstract:  It is well known that the elliptic operators in the divergence form admit Green’s functions that are comparable to those of the Laplace operator, even when the coefficients are just measurable.

However, unlike Green’s function for elliptic operators in the divergence form, Green’s function for nondivergence form elliptic operators does not necessarily have pointwise bounds, even if the domain is smooth and the coefficients are uniformly continuous.

In this talk, I will talk about construction and estimates for Green's functions of nondivergent elliptic operators with continuous coefficients satisfying Dini mean oscillation conditions.

Bio: Seick Kim earned his B.S. in Mathematics in 1997 from Korea Advanced Institute of Science and Technology, and in 2003 he earned his PhD in Mathematics at University of Minnesota, Minneapolis.

Currently he a Professor of Mathematics at Yonsei University, where he has been since 2008. Prior to that he was a Research Fellow at Australian national University (2007-2008) and a Postdoctoral Fellow at University of Missouri, Columbia (2003-2007). From 2016-2017 he was a Visiting Professor at Broan University, a Member at Institut Henri Poincare in June 2015, and a Member at Mathematical Sciences Research Institute in 2005.