Title
Sobolev extension domains
Abstract
In this talk, we study Sobolev extension domains and interpolation inequalities. We first establish an interpolation inequality satisfied by Sobolev extension domains, which leads to applications in mathematical physics. Next, we investigate the relationship between Sobolev extension domains and homogeneous Sobolev extension domains. We also show that, under suitable assumptions, the boundary of a Sobolev extension domain has Lebesgue measure zero. Finally, we characterize Sobolev extension domains through a Bourgain–Brezis–Mironescu (BBM) type inequality.
This talk will be based on joint works with Pekka Koskela, Zheng Zhu, Kaushik Mohanta and Rupert Frank.
