Entire $p$-harmonic functions with an isolated critical point and failure of $C^1$-regularity of the natural gradient

Erno Kauranen, Jarkko Siltakoski

For every $n\ge 2$ and $1<p<\infty$, we show an existence of a nonconstant homogeneous entire $p$-harmonic function whose only critical point is the origin. The angular parts of the…