Electron. J. Diff. Eqns., Vol. 2002(2002), No. 101, pp. 1-22.

On the properties of infinity-harmonic functions and an application to capacitary convex rings

Tilak Bhattacharya

Abstract:
We study positive $\infty$-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 $\infty$-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.

Submitted August 17, 2002. Published November 28, 2002.
Math Subject Classifications: 35J70, 26A16.
Key Words: Viscosity solutions, boundary Harnack inequality, infinity-Laplacian, capacitary functions, convex rings

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Tilak Bhattacharya
Mathematics Department
Bishop's University
Lennoxville, Quebec J1M 1Z7, Canada
e-mail: tbhattac@ubishops.ca

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