Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics for the resolvent equation associated to the game-theoretic
  $p$-laplacian   We consider the (viscosity) solution $u^\varepsilon$ of the elliptic equation
$\varepsilon^2\Delta_p^G u= u$ in a domain (not necessarily bounded),
satisfying $u=1$ on its boundary. Here, $\Delta_p^G$ is the {\it game-theoretic
or normalized $p$-laplacian}. We derive asymptotic formulas for $\varepsilon\to
0^+$ involving the values of $u^\varepsilon$, in the spirit of Varadhan's work
\cite{Va}, and its $q$-mean on balls touching the boundary, thus generalizing
that obtained in \cite{MS-AM} for $p=q=2$. As in a related parabolic problem,
investigated in \cite{BM}, we link the relevant asymptotic behavior to the
geometry of the domain.

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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph