L\'evy-type operators with low singularity kernels: regularity estimates and martingale problem
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:赵国焕(中国科学院数学与系统科学研究院)
:2023-05-11 15:00
:腾讯会议ID:402-263-988(无密码)
报告人:赵国焕(中科院数学与系统科学研究院)
时 间:2023年5月11日下午15:00
地 点:腾讯会议ID:402-263-988(无密码)
内容摘要:
The main focus of this talk is on the linear non-local operator $L$ defined by \begin{align*} L u (x) = \int_{\mathbb{R}^d} (u(x+z)-u(x)) a(x,z)J(z)~d z.\end{align*} Here $J$ is the jumping kernel of a L\'evy process, which exhibits only a low-order singularity near the origin and does not permit standard scaling. To analyze elliptic equations associated with $L$, I will introduce generalized Orlicz-Besov spaces that are specifically tailored for this purpose. Moreover, I will establish certain regularity properties of the solutions to such equations in these spaces. Additionally, I intend to introduce the martingale problem associated with $L$. By exploiting analytic results, we demonstrate the well-posedness of the martingale problem under mild conditions, and establish a new Krylov-type estimate for the corresponding Markov processes. This is based on joint work with Eryan Hu from Tianjin University.
个人简介:
赵国焕,中国科学院数学与系统科学研究院副研究员。主要研究领域为随机分析,马氏过程和非局部算子。2016年博士毕业于北京大学数学科学学院。2016至2018年,在中国科学院数学与系统科学研究院从事博士后研究。2018年至2021年,在德国比勒菲尔德大学从事博士后研究。2022年起在中国科学院应用数学所任职,2022年获国家高层次人才称号。已在 Communications in Mathematical Physics,Transactions of the American Mathematical Society,Journal of Differential Equations, Bernoulli, Stochastic Processes and their Applications等发表十余篇论文。
联系人:陈娴