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• W2922372608 abstract "Building upon the recent results in cite{FoSp17} we provide a thorough description of the free boundary for the fractional obstacle problem in $mathbb{R}^{n+1}$ with obstacle function $varphi$ (suitably smooth and decaying fast at infinity) up to sets of null $mathcal{H}^{n-1}$ measure. In particular, if $varphi$ is analytic, the problem reduces to the zero obstacle case dealt with in cite{FoSp17} and therefore we retrieve the same results: (i) local finiteness of the $(n-1)$-dimensional Minkowski content of the free boundary (and thus of its Hausdorff measure), (ii) $mathcal{H}^{n-1}$-rectifiability of the free boundary, (iii) classification of the frequencies and of the blow-ups up to a set of Hausdorff dimension at most $(n-2)$ in the free boundary. Instead, if $varphiin C^{k+1}(mathbb{R}^n)$, $kgeq 2$, similar results hold only for a distinguished subset of points in the free boundary where the order of contact of the solution and the obstacle is less than $k+1$." @default.
• W2922372608 created "2019-03-22" @default.
• W2922372608 creator A5027009955 @default.
• W2922372608 creator A5039149789 @default.
• W2922372608 date "2019-03-14" @default.
• W2922372608 modified "2023-09-27" @default.
• W2922372608 title "The local structure of the free boundary in the fractional obstacle problem" @default.
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