Geodesic
Extensions from the Sobolev spaces $H^1$ satisfying prescribed Dirichlet boundary conditions
Applications of Mathematics, Tome 49 (2004) no. 5, pp. 405-413.

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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.
DOI : 10.1023/B:APOM.0000048120.75291.a5
Classification : 46E35, 46N40, 65N99
Keywords: extensions satisfying prescribed boundary conditions; Nikolskij extension theorem 
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     title = {Extensions from the {Sobolev} spaces  $H^1$ satisfying prescribed {Dirichlet} boundary conditions},
     journal = {Applications of Mathematics},
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Ženíšek, Alexander. Extensions from the Sobolev spaces  $H^1$ satisfying prescribed Dirichlet boundary conditions. Applications of Mathematics, Tome 49 (2004) no. 5, pp. 405-413. doi : 10.1023/B:APOM.0000048120.75291.a5. http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000048120.75291.a5/

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