報告題目：Existence and uniqueness of limits at infinity for homogeneous Sobolev functions
報 告 人：Khanh Nguyen, Postdoc, Academy of Mathematics and Systems Science Chinese Academy of Science
報告時間：2023年10月10日10:00--11:00
報告地點：騰訊會議 ID：108-063-623
校内聯系人：馬世琪 mashiqi@jlu.edu.cn
報告摘要：We establish the existence and uniqueness of limits at infinity along infinite curves outside a zero modulus family for functions in a homogeneous Sobolev space under the assumption that the underlying space is equipped with a doubling measure which supports a Poincaré inequality. We also characterize the settings where this conclusion is nontrivial. Secondly, we introduce notions of weak polar coordinate systems and radial curves on metric measure spaces. Then sufficient and necessary conditions for existence of radial limits are given. As a consequence, we characterize the existence of radial limits in certain concrete settings.
報告人簡介： Khanh Nguyen received his PhD 2021 at the University of Jyväskylä, Finland under the supervision of Prof. Pekka Koskela. After that, he was a one-year Postdoctoral Researcher at the same institute and then moved to Vietnam working as a Lecturer at the Vietnam National University for 9 months. Since July 2023, he has been working as a Postdoctoral Researcher at AMSS, CAS, China. He is interested in Analysis on metric spaces, especially theories of Sobolev spaces. A part of his research was published in the Journal of Functional Analysis in 2022 and 2023.
