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 $ε>0$.

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