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

We consider the (viscosity) solution of the elliptic equation in a domain (not necessarily bounded), satisfying on its boundary. Here, is the game-theoretic or normalized p-laplacian. We derive asymptotic formulas for involving the values of , in the spirit of Varadhan's work, and its q-mean on balls touching the boundary, thus generalizing that obtained by R. Magnanini and S. Sakaguchi for . As in a related parabolic problem, investigated in a previous work by the authors, we link the relevant asymptotic behavior to the geometry of the domain.