4 problems

Let $p$ be a prime. Consider a variational problem formulated on chain spaces over $\mathbb{Q}_p$, $\mathbb{Z}_p$, and $\mathbb{Z}/p^n\mathbb{Z}$ for $n\geq 1$, all equipped with t…

A variational problem may be formulated on chain spaces with coefficients in $\mathbb{R}$, $\mathbb{Z}$, and $\mathbb{Z}/n\mathbb{Z}$ for $n\geq 2$. Obstructions to the Hasse princ…

A variational problem may be formulated on chain spaces with coefficients in $\mathbb{R}$, $\mathbb{Z}$, and $\mathbb{Z}/n\mathbb{Z}$ for $n\geq 2$. The Hasse principle for variati…

Let $E\subset\mathbb{R}^n$ be a finite-perimeter set with mass $|E|=m$, surface energy … and nonlocal repulsion energy … The binding energy is…