报告题目：Analysis of solutions to fractional Laplace equations

摘要:The fractional Laplacian in Rn is a nonlocal pseudo-differential operator, it has various applications in anomalous diffusion, quasi-geostrophic flows, turbulence, molecular dynamics and so on. In this talk, we will introduce a direct method of moving planes and a sliding method for the fractional Laplacian. We first introduce the key ingredients needed in these methods, such as narrow region principles and maximum principles. Then using semi-linear equations involving the fractional Laplacian, we illustrate how these methods can be employed to obtain monotonicity, symmetry and non-existence of positive solutions.

报告时间：1月13日（周三）上午10:00-11:30

报告地点：腾讯会议ID：740478947

专家介绍：武乐云，西北工业大学博士，目前在上海交通大学从事博士后研究。获得上海市超级博士后资助，入选2020年度香江学者计划，主持博士后基金面上项目一项。近年来，利用移动平面法在偏微分方程领域做出了很多重要工作，研究成果发表在 Adv. Math., DCDS(A) 等国际知名期刊。