Infinity Laplacian equation with strong absorptions

Abstract

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 $\epsilon >0$.

Cited by in corpus (4)

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• Infinity Laplacian equations with singular absorptions
• Geometric regularity estimates for fully nonlinear elliptic equations with free boundaries
• On the supremal version of the Alt-Caffarelli minimization problem