中科院数学与系统科学研究院

数学研究所

学术报告

非线性分析研讨班

报告人：Khanh Nguyen （AMSS）

题  目：Existence and uniqueness of limits at infinity for homogeneous Sobolev functions

时  间：2023.09.20（星期三）10:30-11:20

地  点：思源楼S813

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.