Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A mean value formula for the variational $p$-Laplacian   We prove a new asymptotic mean value formula for the $p$-Laplace operator, $$
\Delta_p u=\text{div}(|\nabla u|^{p-2}\nabla u), $$ valid in the viscosity
sense. In the plane, and for a certain range of $p$, the mean value formula
holds in the pointwise sense. We also study the existence, uniqueness and
convergence of the related dynamic programming principle.

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The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th