On the Properties of Infinity-Harmonic Functions and an Application to Capacitary Convex Rings
Southwest Texas State University, Department of Mathematics
We 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.
Viscosity solutions, Boundary Harnack inequality, Infinity-Laplacian, Capacitary functions, Convex rings
Bhattacharya, 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.
Attribution 4.0 International