Geodesic
On a generalization of Nikolskij's extension theorem in the case of two variables
Applications of Mathematics, Tome 48 (2003) no. 5, pp. 367-404.

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A modification of the Nikolskij extension theorem for functions from Sobolev spaces $H^k(\Omega )$ is presented. This modification requires the boundary $\partial \Omega $ to be only Lipschitz continuous for an arbitrary $k\in \mathbb{N}$; however, it is restricted to the case of two-dimensional bounded domains.
DOI : 10.1023/B:APOM.0000024482.61562.2b
Classification : 46E35, 46E39, 46E99
Keywords: Whitney’s extension; Calderon’s extension; Nikolskij’s extension; modified Nikolskij’s extension in case of 2D-domains with a Lipschitz continuous boundary 
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     title = {On a generalization of {Nikolskij's} extension theorem in the case of two variables},
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Ženíšek, Alexander. On a generalization of Nikolskij's extension theorem in the case of two variables. Applications of Mathematics, Tome 48 (2003) no. 5, pp. 367-404. doi : 10.1023/B:APOM.0000024482.61562.2b. http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000024482.61562.2b/

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