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曹锡华数学论坛
Boundary Regularity for Elliptic Equations
张凯 博士(西北工业大学)
7月24日下午14:00- 15:00  腾讯会议 ID 768 344 368

主持人:何小清 青年研究员
报告时间:7月24日下午14:00- 15:00
报告平台:腾讯会议 ID 768 344 368 (https://meeting.tencent.com/s/uMSxZl1U5K0j)

报告人简介:张凯博士,西北工业大学助理教授,2016年毕业于西安交通大学,导师是李东升教授。张凯的研究方向是偏微分方程理论(主要是正则性理论)。他已经在椭圆偏微分方程的边界正则性方向取得一系列最新的研究成果,在国际一流期刊Archive for Rational Mechanics and Analysis, Journal de Mathématiques Pures et Appliquées, Journal of Differential Equations, Manuscripta Mathematica, Proceedings of the American Mathematical Society, Bulletin of the London Mathematical Society上发表多篇学术论文,主持国家自然科学基金青年项目和陕西省自然科学基础研究计划青年项目各一项。曾获得2019年陕西省优秀博士论文。

报告内容摘要:

This talk investigates the relation between the boundary geometric properties and the boundary regularity of the solutions of elliptic equations. In particular, we prove by a new unified method the pointwise boundary H?lder regularity under proper geometric conditions. “Unified” means that our method is applicable for the Laplace equation, linear elliptic equations in divergence and non-divergence form, fully nonlinear elliptic equations, the p-Laplace equations and the fractional Laplace equations etc. In addition, these geometric conditions are quite general. The key observation in the method is that the strong maximum principle and a scaling argument leads to the H?lder regularity.