Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structure and regularity of the singular set in the obstacle problem for
  the fractional Laplacian   We study the singular part of the free boundary in the obstacle problem for
the fractional Laplacian, \ $\min\bigl\{(-\Delta)^su,\,u-\varphi\bigr\}=0$ in
$\mathbb R^n$, for general obstacles $\varphi$. Our main result establishes the
complete structure and regularity of the singular set. To prove it, we
construct new monotonicity formulas of Monneau-type that extend those in
\cite{GP} to all $s\in(0,1)$.

8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga