Abstract
We present a detailed proof of the density of the set \(C^\infty (\bar \Omega ) \cap V\) in the space of test functions V ⊂ H 1 (Ω) that vanish on some part of the boundary ∂Ω of a bounded domain Ω.
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This work was supported by the grants GAČR 201/03/0570 and MSM 262100001.
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Doktor, P., Ženíšek, A. The density of infinitely differentiable functions in Sobolev spaces with mixed boundary conditions. Appl Math 51, 517–547 (2006). https://doi.org/10.1007/s10492-006-0019-5
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DOI: https://doi.org/10.1007/s10492-006-0019-5