Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Fractional Korn-type inequality for smooth domains and a regularity
  estimate for nonlinear nonlocal systems of equations   In this paper we prove a fractional analogue of the classical Korn's first
inequality. The inequality makes it possible to show the equivalence of a
function space of vector field characterized by a Gagliardo-type seminorm with
'projected difference' with that of a corresponding fractional Sobolev space.
As an application, we will use it to obtain a Caccioppoli-type inequality for a
nonlinear system of nonlocal equations, which in turn is a key ingredient in
applying known results to prove a higher fractional differentiability result
for weak solutions of the nonlinear system of nonlocal equations. The
regularity result we prove will demonstrate that a well-known self-improving
property of scalar nonlocal equations will hold for strongly coupled systems of
nonlocal equations as well.

22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an