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The density of infinitely differentiable functions in Sobolev spaces with mixed boundary conditions. (English) Zbl 1164.46322

Summary: 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  \(\Omega \).

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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References:

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