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The density of infinitely differentiable functions in Sobolev spaces with mixed boundary conditions

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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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Authors and Affiliations

  1. Českolipská 12, 190 00, Prague 9, Czech Republic

    Pavel Doktor

  2. Department of Mathematics FME, Technická 2, 616 69, Brno, Czech Republic

    Alexander Ženíšek

Authors
  1. Pavel Doktor
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  2. Alexander Ženíšek
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Additional information

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

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