Quantitative periodic homogenization for symmetric non-local stable-like operators

主讲人：陈昕 上海交通大学教授

时间：2023年5月13日9：30

地点：会议中心2号报告厅

举办单位：数理学院

主讲人介绍：陈昕，上海交通大学，教授。2011年博士毕业于华威大学，师从李雪梅教授。主要研究领域是随机分析，包括泛函不等式，流型上的随机分析，跳过程的位势理论，随机均值化等。在国际知名数学期刊AoP, PTRF, CMP, Math Ann.等发表了多篇学术论文。

内容介绍：In this paper, we establish a quantitative version of homogenization for symmetric α-stable-like operators with periodic coefficients. In particular, the convergence rate for the solutions of associated Dirichlet problems on bounded domain D is of order ε^((2-α)/2) 1_({α∈(1,2)})+ε^(α/2) 1_({α∈(0,1)})+ε^(1/2) 〖|logε|〗^2 1_({α=1}), while, when the solution of limit equation belongs to C_c^2 (D), the convergence rate becomes ε^((2-α)) 1_({α∈(1,2)})+ε^α 1_({α∈(0,1)})+ε〖|logε|〗^2 1_({α=1}). This indicates that the decay behaviors of the solution of limit equation near the boundary will make the convergence rate in the homogenization slower. This talk is based on a joint work with Zhen-qing Chen, Takashi Kumagai and Jian Wang.