Lewis, John L.

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

Electron. J. Differ. Equ. 1994(3), (1994)


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.

Mathematics Subject Classification

35J70, 35B05


p-harmonic functions, p-Laplacian, quasiregular mappings