Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Reaction-diffusion equations for infinity Laplacian
Publication Date:	2019-07-17
Authors:	- Nicolau Matiel Lunardi Diehl - Rafayel Teymurazyan
Abstract:	We derive sharp regularity for viscosity solutions of an inhomogeneous infinity Laplace equation across the free boundary, when the right hand side of the equation does not change sign and satisfies a certain growth condition. We prove geometric regularity estimates for solutions and conclude that the free boundary is a porous set and hence has zero Lebesgue measure. Additionally, we derive a Liouville type theorem. When the right hand side is comparable to power function of degree three, we show that if a non-negative viscosity solution vanishes at a point, then it has to vanish everywhere.
Institution:	DMUC 19-26
Online version:	http://www.mat.uc.pt...prints/eng_2019.html
Download:	Not available