Geodesic
The density of infinitely differentiable functions in Sobolev spaces with mixed boundary conditions
Applications of Mathematics, Tome 51 (2006) no. 5, pp. 517-547.

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We present a detailed proof of the density of the set $C^\infty (\overline{\Omega })\cap V$ in the space of test functions $V\subset H^1(\Omega )$ that vanish on some part of the boundary $\partial \Omega $ of a bounded domain $\Omega $.
DOI : 10.1007/s10492-006-0019-5
Classification : 46E35, 46N40
Keywords: density theorems; finite element method 
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     title = {The density of infinitely differentiable functions in {Sobolev} spaces with mixed boundary conditions},
     journal = {Applications of Mathematics},
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     publisher = {mathdoc},
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Doktor, Pavel; Ženíšek, Alexander. The density of infinitely differentiable functions in Sobolev spaces with mixed boundary conditions. Applications of Mathematics, Tome 51 (2006) no. 5, pp. 517-547. doi : 10.1007/s10492-006-0019-5. http://geodesic.mathdoc.fr/articles/10.1007/s10492-006-0019-5/

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