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arXiv · 1601.00957

Infinity Laplacian equation with strong absorptions

Damião J. Araújo·Raimundo Leitão·Eduardo V. Teixeira
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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 $\epsilon>0$.

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Damião J. Araújo, Raimundo Leitão, Eduardo V. Teixeira. 2016-01-05. Infinity Laplacian equation with strong absorptions. https://doi.org/10.1016/j.jfa.2015.12.012

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