Sharp geometric conditions for Sobolev extension operators
调和分析及其应用专题报告
报告题目(Title)：Sharp geometric conditions for Sobolev extension operators
报告人(Speaker)：Sebastian Bechtel博士 (Université Paris-Saclay, France)
地点(Place)：后主楼1124
时间(Time)：2026年1月19日（周一）15:00-17:00
邀请人(Inviter)：杨大春
报告摘要
It is a classical question in the theory of Sobolev spaces on which open sets it is possible to construct a linear extension operator for corresponding Sobolev spaces. Easy examples such as a ball with a slit show that such a construction is not always possible. However, in the literature there were given many sufficient conditions, like boundaries that are sufficiently smooth or Jones’ Epsilon-Delta-condition, under which the question can be answered in the affirmative. To the contrary, if we only consider Sobolev spaces of functions with a (vanishing) Dirichlet boundary condition, extension by zero is possible, which requires no geometric quality at all. In this talk, it is our goal to investigate Sobolev spaces of functions that vanish only on a part of the boundary, and we will present conditions that allow to construct a Sobolev extension operator in this constellation that are sharp at the interface between the two boundary parts.
