Electronic Journal of Differential Equations,
Vol. 1994(1994), No. 03, pp. 1-4.

Title: On critical points of $p$ harmonic functions in the plane

Author: John L. Lewis (Univ. of Kentucky, Lexington, USA)

Abstract: We show that if $ u $ is a $ p $ harmonic  function,
$ 1 < p < \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 deg$P - 1$ 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.