Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence between distributional and viscosity solutions for the
  double-phase equation   We investigate the different notions of solutions to the double-phase
equation $$ -\dive(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du)=0, $$ which is characterized
by the fact that both ellipticity and growth switch between two different types
of polynomial according to the position. We introduce the
$\mathcal{A}_{H(\cdot)}$-harmonic functions of nonlinear potential theory, and
then show that $\mathcal{A}_{H(\cdot)}$-harmonic functions coincide with the
distributional and viscosity solutions, respectively. This implies that the
distributional and viscosity solutions are exactly the same.

15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ