Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 35, 2010, 309-320

A JORDAN SOBOLEV EXTENSION DOMAIN

Pekka Koskela, Dachun Yang and Yuan Zhou

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland; pkoskela 'at' maths.jyu.fi

Beijing Normal University, School of Mathematical Sciences
Laboratory of Mathematics and Complex Systems, Ministry of Education
Beijing 100875, P.R. China; dcyang 'at' bnu.edu.cn

Beijing Normal University, School of Mathematical Sciences
Laboratory of Mathematics and Complex Systems, Ministry of Education
Beijing 100875, P.R. China; yuanzhou 'at' mail.bnu.edu.cn
and University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland; yuzhou 'at' jyu.fi

Abstract. Let 1 < q < 2. In this paper, we construct a Jordan domain G_q \subset R² such that G_q \in Ext_p if and only if 1 \le p < q, and R²\G_q \in Ext_s if and only if q/(q - 1) < s \le \infty.

2000 Mathematics Subject Classification: Primary 46E35.

Key words: Sobolev space, Sobolev extension, planar Lipschitz extension domain.

Reference to this article: P. Koskela, D. Yang and Y. Zhou: A Jordan Sobolev extension domain. Ann. Acad. Sci. Fenn. Math. 35 (2010), 309-320.

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doi:10.5186/aasfm.2010.3519