Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity results for a class of nonlinear fractional Laplacian and
  singular problems   In this article, we investigate the existence, uniqueness, nonexistence, and
regularity of weak solutions to the nonlinear fractional elliptic problem of
type $(P)$ (see below) involving singular nonlinearity and singular weights in
smooth bounded domain. We prove the existence of weak solution in
$W_{loc}^{s,p}(\Omega)$ via approximation method. Establishing a new comparison
principle of independent interest, we prove the uniqueness of weak solution for
$0 \leq \delta< 1+s- \frac{1}{p}$ and furthermore the nonexistence of weak
solution for $\delta \geq sp.$ Moreover, by virtue of barrier arguments we
study the behavior of minimal weak solution in terms of distance function.
Consequently, we prove H\"older regularity up to the boundary and optimal
Sobolev regularity for minimal weak solutions.

3
The categories of this paper are: physics
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org