分析、偏微分方程与动力系统讨论班(2026秋季第2讲)

Whitney extension problem for fractional Sobolev spaces

孙一兵

(北京师范大学)

时间与地点：10月21日（周三）15:30-16:30（北京时间);

沙河主楼E502

摘要: We consider the Whitney extension problem for continuous fractional Sobolev spaces, i.e., given a continuous function defined on a closed subset, whether can we extend this function to the global space such that the extended function belongs to the continuous fractional Sobolev spaces? The problem of such type was started from H. Whitney in 1934 when he considered the case for differentiable functions. As for the case of Sobolev space, Shvartsman gave the characterization of the restriction space and proved that there exists a bounded linear extension operator. Partially motivated by him, and combining the pointwise characterization, we extended the criteria to fractional Sobolev space. Moreover, it also works for Besov and Trieble-Lizorkin space.

报告人简介: 孙一兵，北京师范大学数学科学学院博士研究生

邀请人：朱政

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