Bhattacharya, Tilak2020-09-102020-09-102002-11-28Bhattacharya, T. (2002). On the properties of infinity-harmonic functions and an application to capacitary convex rings. <i>Electronic Journal of Differential Equations, 2002</i>(101), pp. 1-22.1072-6691https://hdl.handle.net/10877/12565We study positive ∞-harmonic functions in bounded domains. We use the theory of viscosity solutions in this work. We prove a boundary Harnack inequality and a comparison result for such functions near a flat portion of the boundary where they vanish. We also study ∞-capacitary functions on convex rings. We show that the gradient satisfies a global maximum principle, it is nonvanishing outside a set of measure zero and the level sets are star-shaped.Text22 pages1 file (.pdf)enAttribution 4.0 InternationalViscosity solutionsBoundary Harnack inequalityInfinity-LaplacianCapacitary functionsConvex ringsArticle