Dachun Yang

Capacitary-Distance Hardy Inequality

Let $n\ge3$, $\Omega\subset\mathbb R^n$ be an open set, $F:=\mathbb R^n\setminus\Omega$, and $\alpha\in(0,\infty)$. For any $x\in\Omega$, we define the capacitary distance \begin{align*} d_\alpha(x) := \inf\left\{ r>0: \operatorname{cap}(\overline{F\cap B(x,r)}) \ge \alpha\operatorname{cap}(B(\mathbf0,r)) \right\}. \en...