回复：Need help for two qns on harmonic functions

1. Use gradient estimates for harmonic function,
|grad^k u(x)|<=max_{B(0, 2|x|)} |u(y)|/|x|^k
You can immediately show that grad^p u(x) is a bounded harmonic function, therefore a constant.

2. just by gradient estimates as well, assume R=1, then do the problem. Reference: Elliptic Partial Differential Equations by Qing Han&Fanghua Lin