2020/05/04 by Diehl, Nicolau M. L., Teymurazyan, Rafayel · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2005.01551
We derive sharp regularity for viscosity solutions of an inhomogeneous infinity Laplace equation across the free boundary, when the right hand side does not change sign and satisfies a certain growth condition. We prove geometric regularity estimates for solutions and conclude that once the source term is comparable to a homogeneous function, then the free boundary is a porous set and hence, has zero Lebesgue measure. Additionally, we derive a Liouville type theorem. When near the origin the right hand side grows not faster than third degree homogeneous function, we show that if a non-negative viscosity solution vanishes at a point, then it has to vanish everywhere.