Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elliptic equations involving the 1--Laplacian and a total variation term
  with $L^{N,\infty}$--data   In this paper we study, in an open bounded set $\Omega\subset\mathbb R^N$
with Lipschitz boundary $\partial\Omega$, the Dirichlet problem for a nonlinear
singular elliptic equation involving the $1$--Laplacian and a total variation
term, that is, the inhomogeneous case of the equation appearing in the level
set formulation of the inverse mean curvature flow. Our aim is twofold. On the
one hand, we consider data belonging to the Marcinkiewicz space
$L^{N,\infty}(\Omega)$, which leads to unbounded solutions. So, we have to
begin introducing the suitable notion of unbounded solution to this problem.
Moreover, examples of explicit solutions are shown. On the other hand, this
equation allows us to deal with many related problems having a different
gradient term. It is known that the total variation term induces a regularizing
effect on existence, uniqueness and regularity. We focus on analyzing whether
those features remain true when general gradient terms are taken. Roughly
speaking, the bigger $g$, the better the properties of the solution.

24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph