Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong Liouville theorems for discrete averaging operators   We introduce averaging operators on lattices $\mathbb{Z}^d$ and study the
Liouville property for the related discrete PDEs, enclosing the discrete
harmonic, $p$-harmonic, $p$-harmonious and $\infty$-harmonic functions. Our
approach generalizes a previous elementary argument for the discrete harmonic
case and provides an alternative proof for $p$-harmonic functions on
$\mathbb{Z}^2$.

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The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con