Electron. J. Diff. Eqns., Vol. 1994(1994), No. 03, pp. 1-4.

On Critical Points of $p$ Harmonic Functions in the Plane

John L. Lewis

We show that if u is a p harmonic function, 1 less than p less than infty, in the unit disk and equal to a polynomial P of positive degree on the boundary of this disk, then $ \nabla u $ has at most degP - 1 zeros in the unit disk.

Submitted March 30, 1994. Published July 6, 1994.
Math Subject Classification: 35J70, 35B05.
Key Words: p-harmonic functions, p-Laplacian, quasiregular mappings.

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John L Lewis
Department of Mathematics, University of Kentucky
Lexington, Kentucky 40506-0027, USA
e-mail: john@ms.uky.edu
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