Speaker: Tuoc Phan, Professor of Mathematics, University of Tennessee at Knoxville
Title: Recent results on linear elliptic and parabolic equations with singular or degenerate coefficients
Abstract: The talk is about the analysis theory for second order linear elliptic and parabolic equations. We particularly focus on the regularity estimates, existence, and uniqueness of solutions to classes of equations whose coefficients are just measurable. Several classical results when the coefficients are uniformly elliptic and bounded will be reviewed and explained. Motivations to study the equations whose coefficients are neither uniformly elliptic nor bounded will be addressed. Some recent results and developments will be reported. Important open research directions will be mentioned. The main results discussed in talk are based on several papers which are the joint work with Hongjie Dong (Brown University) and with Hung Tran (University of Wisconsin at Madison).