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arXiv · 2002.08656

The extension problem for fractional Sobolev spaces with a partial vanishing trace condition

Sebastian Bechtel
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Abstract

We construct whole-space extensions of functions in a fractional Sobolev space of order $s\in (0,1)$ and integrability $p\in (0,\infty)$ on an open set $O$ which vanish in a suitable sense on a portion $D$ of the boundary $\partial O$ of $O$. The set $O$ is supposed to satisfy the so-called interior thickness condition in $\partial O \setminus D$, which is much weaker than the global interior thickness condition. The proof works by means of a reduction to the case $D=\emptyset$ using a geometric construction.

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Sebastian Bechtel. 2020-02-20. The extension problem for fractional Sobolev spaces with a partial vanishing trace condition. https://doi.org/10.1007/s00013-021-01594-0

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