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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… Click to show full 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.
Keywords:
spaces partial;
fractional sobolev;
condition;
problem fractional;
sobolev spaces;
extension problem
Journal Title: Archiv der Mathematik
Year Published: 2021
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Journal Title: Archiv der Mathematik
Year Published: 2021
Link to full text (if available)
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recommendations!