3 problems

Let $d,n\in\mathbb{N}$ and $1<p<\infty$. Let $h\colon\Omega\to\mathbb{R}^n$ be $p$-harmonic on an open set $\Omega\subset\mathbb{R}^d$, and let $V$ denote the standard nonlinear tr…

Let $u$ solve the one-dimensional $p$-parabolic boundary-value problem … on $(-1,1)\times(0,T)$ with boundary values $u(-1,t)=0$, $u(1,t)=1$, and initial value…

Non-vanishing conjecture. If $\Delta_pu=0$ for $p>1$ and $p\ne2$, then $u\equiv 0$.