Paris/Berkeley/Bonn/Zürich Analysis Seminar: Planar Sobolev extension domains

Seminar | February 22 | 9:10-10 a.m. | 238 Sutardja Dai Hall

 Yi Zhang, University of Bonn

 Department of Mathematics

A domain $\Omega \subset \mathbb R^2$ is called a $W^{1,\,p}$-extension domain if it admits an extension operator $E\colon W^{1,\,p}(\Omega ) \to W^{1,\,p}(\mathbb R^2)$ with controlled norm. A full geometric characterization of these domains for $p=2$ was given around 1980. The case $p >2$ was finally solved by P. Shvartsman in 2010. We discuss the remaining cases, and give some new understandings of the geometric characterizations from the point of view of (classical) complex analysis.