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Keywords:
Whitney’s extension; Calderon’s extension; Nikolskij’s extension; modified Nikolskij’s extension in case of 2D-domains with a Lipschitz continuous boundary
Whitney’s extension; Calderon’s extension; Nikolskij’s extension; modified Nikolskij’s extension in case of 2D-domains with a Lipschitz continuous boundary
Summary:
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.
References:
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