# Article

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Keywords:
extensions satisfying prescribed boundary conditions; Nikolskij extension theorem
Summary:
Extensions from $H^1(\Omega _P)$ into $H^1(\Omega )$ (where $\Omega _P\subset \Omega$) are constructed in such a way that extended functions satisfy prescribed boundary conditions on the boundary $\partial \Omega$ of $\Omega$. The corresponding extension operator is linear and bounded.
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