Asymptotics for the resolvent equation associated to the game-theoretic <i>p</i>-laplacian

Abstract

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 on balls touching the boundary, thus generalizing that obtained by R. Magnanini and S. Sakaguchi for p=q=2. 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.

Locations

• Florence Research (University of Florence) - View - PDF
• Applicable Analysis - View