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.
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
Show me the PDF file (325K), TEX file, and other files for this article.
|Tilak Bhattacharya |
Lennoxville, Quebec J1M 1Z7, Canada
Return to the EJDE web page