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On a generalization of Nikolskij’s extension theorem in the case of two variables. (English) Zbl 1099.46022

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.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables
46E99 Linear function spaces and their duals
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References:

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