【4月19日】Non-negative solutions to fractional Laplace equations with isolated singularity

2019-04-12

时间:2019.4.19 15:30-16:30

地点:理学院楼331

主讲人:李从明

使用语言:中文,英文

主讲人简介:

上海交通大学数学科学学院院长、讲席教授, 国家千人学者,主要研究非线性偏微分方程、变分法、微分几何、非线性分析、流体动力学。李从明教授博士毕业于纽约大学柯朗数学科学研究所,师从国际数学界分析学大师Louis Nirenberg,在几何分析、流体力学、非线性偏微分和积分方程与方程组,及其相关应用领域做出了一流的工作。突破古典的研究模式,改进和发展了古典的数学方法,所研究出来的成果具有极强的原创性和独特性。已发表SCI论文50余篇,包括国际顶尖期刊Proceedings of the National Academy of Sciences, Annals of Mathematics, Inventiones Mathematicae, Communications on Pure and Applied Mathematics, Journal of Differential Geometry, Advances in Mathematics等等。被SCI引用累计2700余次,发表著作1部。

活动内容摘要:

We study singular solutions of linear problems with fractional Laplacian.

First, we establish B\^{o}cher type theorems on a punctured ball via distributional approach.  Then, we develop a few interesting maximum principles on a punctured ball. Our distributional approach only requires the basic $L_{{\rm loc}}^1$-integrability. Furthermore, several basic lemmas are introduced to unify the treatments of Laplacian and fractional Laplacian. This is a joint work with C. Liu, Z. Wu and H. Xu.