Hajłasz, Piotr; Martio, Olli Traces of Sobolev functions on fractal type sets and characterization of extension domains. (English) Zbl 0877.46025 J. Funct. Anal. 143, No. 1, 221-246 (1997). 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 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 A. Jonsson and H. Wallin, “Function spaces on subsets of \(\mathbb{R}^n\)” (1984). Reviewer: S.Wedrychowicz (Rzeszów) Cited in 1 ReviewCited in 66 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:traces of Sobolev functions; smooth submanifolds; fractal subsets; John domain Citations:Zbl 0859.46022 PDFBibTeX XMLCite \textit{P. Hajłasz} and \textit{O. Martio}, J. Funct. Anal. 143, No. 1, 221--246 (1997; Zbl 0877.46025) Full Text: DOI Link