报告题目：Harnack inequality for singular or degenerate parabolic equations in non-divergence form
报 告 人：方俊元
所在单位：University of Tennessee, Knoxville
报告时间：2024年12月26日 9:00-10:00
报告地点：数学楼一楼第二报告厅
校内联系人：聂元元 nieyy@jlu.edu.cn
报告摘要：In this talk, we discuss about a class of linear parabolic equations in non-divergence form, in which the leading coefficients are measurable and they can be singular or degenerate as a weight belonging to the $A_{1+\frac{1}{n}}$ class of Muckenhoupt weights. Krylov-Safonov Harnack inequality for solutions is proved under some smallness assumption on a weighted mean oscillation of the weight. To prove the result, we introduce a class of generic weighted parabolic cylinders and the smallness condition on the weighted mean oscillation of the weight through which several growth lemmas are established. Additionally, a perturbation method is used and the parabolic Aleksandrov-Bakelman-Pucci type maximum principle is crucially applied to suitable barrier functions to control the solutions. As corollaries, H\"{o}lder regularity estimates of solutions with respect to a quasi-distance, and a Liouville type theorem will be presented in the talk.
This talk is based on the joint work with Sungwon Cho and Tuoc Phan.
报告人简介：方俊元，现为田纳西大学诺克斯维尔分校在读博士生，2020年硕士毕业于首都师范大学。主要从事退化型椭圆和抛物方程的正则性研究，以及变分法的相关问题。
