We consider the (viscosity) solution $u^e$ of the elliptic equation $e^2De_p^G u= u$ in a domain (not necessarily bounded), satisfying $u=1$ on its boundary. Here, $De_p^G$ is the {it game-theoretic or normalized $p$-laplacian}. We derive asymptotic formulas for $e o 0^+$ involving the values of $u^e$, 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.

Asymptotics for the resolvent equation associated to the game-theoretic p-laplacian / Berti, D., Magnanini, R.. - In: APPLICABLE ANALYSIS. - ISSN 0003-6811. - STAMPA. - 98:(2019), pp. 1827-1842. [10.1080/00036811.2018.1466283]

Asymptotics for the resolvent equation associated to the game-theoretic p-laplacian

Berti D.;Magnanini R.
2019

Abstract

We consider the (viscosity) solution $u^e$ of the elliptic equation $e^2De_p^G u= u$ in a domain (not necessarily bounded), satisfying $u=1$ on its boundary. Here, $De_p^G$ is the {it game-theoretic or normalized $p$-laplacian}. We derive asymptotic formulas for $e o 0^+$ involving the values of $u^e$, 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.
2019
98
1827
1842
Berti, D., Magnanini, R.
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1125561
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