Bounded Approximation Property for Sobolev spaces on simply-connected planar domains

preprint2014arXivOpen access

We show that Sobolev space $W^1_1(Ω)$ of any planar one-connected domain $Ω$ has the Bounded Approximation property. The result holds independently from the properties of the boundary of $Ω$ . The prove is based on a new decomposition of a planar domain.

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Bounded Approximation Property for Sobolev spaces on simply-connected planar domains

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