Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Potential estimates and quasilinear parabolic equations with measure
  data   In this paper, we study the existence and regularity of the quasilinear
parabolic equations: $$u_t-\operatorname{div}(A(x,t,\nabla u))=B(u,\nabla
u)+\mu,$$ in either $\mathbb{R}^{N+1}$ or $\mathbb{R}^N\times(0,\infty)$ or on
a bounded domain $\Omega\times (0,T)\subset\mathbb{R}^{N+1}$ where $N\geq 2$.
In this paper, we shall assume that the nonlinearity $A$ fulfills standard
growth conditions, the function $B$ is a continuous and $\mu$ is a radon
measure. Our first task is to establish the existence results with $B(u,\nabla
u)=\pm|u|^{q-1}u$, for $q>1$. We next obtain global weighted-Lorentz,
Lorentz-Morrey and Capacitary estimates on gradient of solutions with $B\equiv
0$, under minimal conditions on the boundary of domain and on nonlinearity $A$.
Finally, due to these estimates, we solve the existence problems with
$B(u,\nabla u)=|\nabla u|^q$ for $q>1$

11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat