题目：Harnack inequality for singular or degenerate parabolic equations in non-divergence form    

报告人：方俊元博士（University of Tennessee, Knoxville）    

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.  

报告时间：2024年12月19日（周四）上午10:00-11:00

报告地点：教二楼727  

联系人：刘兆理