Traces of Sobolev functions on fractal type sets and characterization of extension domains
The authors describe traces of Sobolev functions \(u\in W^{1,p}(\mathbb{R}^n)\), \(1<p\leq\infty\), on certain subsets of \(\mathbb{R}^n\) in terms of Sobolev spaces on metric spaces [see \textit{P. Hajłasz}, Potential Anal. 5, No. 4, 403-415 (1996; Zbl 0859.46022)]. Their results apply to smooth submanifolds, fractal subsets, as well to open subsets of \(\mathbb{R}^n\). In particular if \(\Omega\subset\mathbb{R}^n\) is a John domain, then the authors characterize those \(W^{1,p}(\Omega)\) functions which can be extended to \(W^{1,p}(\mathbb{R}^n)\). In the case of traces on fractal subsets their results are related to those of \textit{A. Jonsson} and \textit{H. Wallin}, ``Function spaces on subsets of \(\mathbb{R}^n\)'' (1984).
scientific article; zbMATH DE number 997641