Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost minimizers for a singular system with free boundary   In this paper we study vector-valued almost minimizers of the energy
functional $$
  \int_D\left(|\nabla\mathbf{u}|^2+2|\mathbf{u}|\right)\,dx .
  $$ We establish the regularity for both minimizers and the "regular" part of
the free boundary. The analysis of the free boundary is based on Weiss-type
monotonicity formula and the epiperimetric inequality for the energy
minimizers.

24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph