3 problems

Higher-order Rellich inequality conjecture. One has

Let $G$ be a graph of polynomial growth with homogeneous dimension $N\geq 3$. For the discrete $p$-biharmonic equation … where $1<p<N/2$, and for the discrete Lane–Emden system … w…

Asymptotic Faber–Krahn shape conjecture. After possibly translating the $G_n$, the Hausdorff distance between $G_n^*$ and $D$ converges to $0$ as $n\to\infty$.