## 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:

 4.6e+36 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

### Keywords:

density theorems; finite element method
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### References:

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