Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry results for critical anisotropic $p$-Laplacian equations in
  convex cones   Given $n \geq 2$ and $1<p<n$, we consider the critical $p$-Laplacian equation
$\Delta_p u + u^{p^*-1}=0$, which corresponds to critical points of the Sobolev
inequality. Exploiting the moving planes method, it has been recently shown
that positive solutions in the whole space are classified. Since the moving
plane method strongly relies on the symmetries of the equation and the domain,
in this paper we provide a new approach to this Liouville-type problem that
allows us to give a complete classification of solutions in an anisotropic
setting. More precisely, we characterize solutions to the critical
$p$-Laplacian equation induced by a smooth norm inside any convex cone. In
addition, using optimal transport, we prove a general class of (weighted)
anisotropic Sobolev inequalities inside arbitrary convex cones.

19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics