Infinity Laplacian equation with strong absorptions

We study regularity properties of solutions to reaction-diffusion equations ruled by the infinity laplacian operator. We focus our analysis in models presenting plateaus, i.e. regions where a non-negative solution vanishes identically. We obtain sharp geometric regularity estimates for solutions along the boundary of plateaus sets. In particular we show that the $(n-ϵ)$-Hausdorff measure of the plateaus boundary is finite, for a universal number $ϵ>0$.