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arXiv · 1801.02824

A density result for homogeneous Sobolev spaces on planar domains

Debanjan Nandi·Tapio Rajala·Timo Schultz
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Abstract

We show that in a bounded simply connected planar domain $\Omega$ the smooth Sobolev functions $W^{k,\infty}(\Omega)\cap C^\infty(\Omega)$ are dense in the homogeneous Sobolev spaces $L^{k,p}(\Omega)$.

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Debanjan Nandi, Tapio Rajala, Timo Schultz. 2018-01-09. A density result for homogeneous Sobolev spaces on planar domains. https://arxiv.org/abs/1801.02824

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