Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted $W^{1,p}$- estimates for weak solutions of degenerate elliptic
  equations with coefficients degenerate in one variable   This paper studies the Sobolev regularity of weak solution of degenerate
elliptic equations in divergence form $\text{div}[\mathbf{A}(X) \nabla u] =
\text{div}[\mathbf{F}(X)]$, where $X = (x,y) \in \mathbb{R}^{n} \times
\mathbb{R}$ . The coefficient matrix $\mathbf{A}(X)$ is a symmetric, measurable
$(n+1) \times (n+1)$ matrix, and it could be degenerate or singular in the one
dimensional $y$-variable as a weight function in the Muckenhoupt class $A_2$ of
weights. Our results give weighted Sobolev regularity estimates of
Calder\'{o}n-Zygmund type for weak solutions of this class of singular,
degenerate equations. As an application of these estimates, we establish global
Sobolev regularity estimates for solutions of the spectral fractional elliptic
equation with measurable coefficients. This result can be considered as the
Sobolev counterpart of the recently established Schauder regularity theory of
fractional elliptic equations.

12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph