Capacity & Perimeter from $α$-Hermite Bounded Variation

Abstract

Let $\mathcal{H}_α=Δ-(α-1)|x|^α$ be an $[1,\infty)\niα$-Hermite operator for the hydrogen atom located at the origin in $\mathbb R^d$. In this paper, we are motivated by the classical case $α=1$ to investigate the space of functions with $α$-{\it Hermite Bounded Variation} and its functional capacity and geometrical perimeter.

36 pages