Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 101, pp. 1-22.

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

Author: Tilak Bhattacharya (Bishop's Univ., Lennoxville, Canada)
         
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