偏微分方程研讨班：Regularity theory for the Dirichlet problem of porous media equations and fast diffusion equations

中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：Prof. Jingang Xiong（Beijing Normal University）

题  目：Regularity theory for the Dirichlet problem of porous media equations and fast diffusion equations

时  间：2022.10.20（星期四）10:00-11:00

地  点：思源楼S315

摘  要：It was proved in 1980s that nonnegative solutions of the homogeneous Dirichlet problem of porous media equations and fast diffusion equations are Holder continuous. Due to the loss of uniform parabolicity near the boundary, the higher order regularity was left unsolved. It was listed as the first unproved problem by Berryman-Holland 1980 for the fast diffusion regime. In this talk, I will present our recent complete solution to this problem. This is based on a series of work with T. Jin as well as a most recent one with T. Jin and X. Ros-Oton.