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 $(n-\epsilon)$-Hausdorff measure of the plateaus boundary is finite, for a universal number $\epsilon>0$. 
Dami\~ao J. Ara\'ujo, Raimundo Leit\~ao and Eduardo V. Teixeira
math.AP math-ph math.MP