4 problems

For a graph with fixed boundary values, consider the $\ell^p$-energy minimizing dynamics and let the $\epsilon$-approximation time denote the time required to reach $\epsilon$-appr…

Let $(K,d,m)$ be the Sierpiński carpet, let $p=d_{\mathrm{ARC}}(K,d)$ be an attained Ahlfors regular conformal dimension, and let $\Gamma_p\langle f\rangle$ denote the $p$-energy m…

Let $u_p$ be $p$-harmonic functions and let $u_\infty$ be the corresponding infinity-harmonic limit, with the functions considered in a setting where their gradients are positive.…

Let $1 < p \in \mathbb{R}$ and let $X$ be a metric measure space. Let $\Delta_p(X)$ denote the $p$-harmonic boundary of $X$, and let $BD^p(X)$ and $HBD^p(X)$ denote the bounded Roy…