Asymptotics for the resolvent equation associated to the game-theoretic <i>p</i>-laplacian
Asymptotics for the resolvent equation associated to the game-theoretic <i>p</i>-laplacian
We consider the (viscosity) solution uε of the elliptic equation ε2ΔpGu=u in a domain (not necessarily bounded), satisfying u=1 on its boundary. Here, ΔpG is the game-theoretic or normalized p-laplacian. We derive asymptotic formulas for ε→0+ involving the values of uε, in the spirit of Varadhan's work, and its q-mean …