For almost every obstacle, the degenerate part of the free boundary in the fractional obstacle problem vanishes up to dimension 3 for every s in (0,1).
A note on the frequency gaps between integers in the thin obstacle problem
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abstract
We give a simple proof of the fact that - in all dimensions - there are no homogeneous solutions to the thin obstacle problem with frequency $\lambda$ belonging to intervals of the form $(2k,2k+1)$, $k \in \mathbb{N}$. In particular, there are no frequencies in the interval $(2,3)$.
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Generic regularity of free boundaries in the obstacle problem for the fractional Laplacian
For almost every obstacle, the degenerate part of the free boundary in the fractional obstacle problem vanishes up to dimension 3 for every s in (0,1).