## On critical points of $p$ harmonic functions in the plane

### Summary

Summary: 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.

35J70, 35B05

### Keywords/Phrases

p-harmonic functions, p-Laplacian, quasiregular mappings