报告I：Calderon-Zygmund estimates for elliptic equations on non-smooth domains

报告II：椭圆偏微分方程的CZ估计

摘要I：Calderon-Zygmund estimates play a key role in the regularity of elliptic and parabolic equations, which give the $L^p$ integral estimates for the second order derivatives of the solutions. In this talk, we will establish Calderon-Zygmund estimates for elliptic equations on C^{1,\alpha} domains. The classical method, straightening the boundary, is not applicable since the domain is not C^{1,1} which is the standard assumption to derive the estimates. Both linear and fully nonlinear equations will be considered. Our main idea is to use Whitney cover lemma to transfer the boundary estimates to the interior estimates.

摘要II：CZ估计是偏微分方程的重要技术，本报告中，我们将针对一类特殊区域上的椭圆偏微分方程的正则性展开讨论，最终给出好的估计。

时间：2022.5.13  9:00-9:55     11:00-11:55

地点：腾讯会议426-929-922

报告人简介：李东升，西安交通大学数学系教授，博士生导师。历任西安交通大学数学与统计学院院长助理，西安交通大学应用数学系、数学系系主任，陕西省数学会常务理事兼副秘书长。长期从事偏微分方程正则性理论方面的研究，目前发表科研论文60余篇；主持国家自然科学基金7项；获教育部科技进步二等奖一项，陕西省科技进步二等奖两项，陕西省教育厅科学技术一等奖一项；获“三秦人才津贴”