Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The local structure of the free boundary in the fractional obstacle
  problem   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 $\varphi\in C^{k+1}(\mathbb{R}^n)$, $k\geq 2$, 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 $k+1$.

30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom