Sobolev extension domains and Poincaré inequalities

We investigate which domains in $\mathbb{R}^n$ allow extensibility of Sobolev functions. Such domains are called $W^{\{m,p\}}$ extension domains, we show that under mild hypothesis on the extension operator that these domains are equivalent to domains satisfying the local Poincaré inequality.

Friday, February 2, 2024 - 14:00 to 15:00

Thackeray Hall Room 703

Speaker Information
Ahmed Alshammari
Graduate Student
University of Pittsburgh