On the Properties of Infinity-Harmonic Functions and an Application to Capacitary Convex Rings
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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.
CitationBhattacharya, T. (2002). On the properties of infinity-harmonic functions and an application to capacitary convex rings. Electronic Journal of Differential Equations, 2002(101), pp. 1-22.
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