Author

Jie Xiao

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Preprint Aug 2026

Capacitary Trapping and Brownian Escape: A Sharp Hardy Principle for Absorbing Media

We study Brownian motion killed upon exiting arbitrary open sets $\Omega\subset\mathbb R^n$, $n\in[3,\infty)\cap\mathbb N$. Let $\alpha\in(0,1]$. The infimal radius $d_\alpha(x)$ at which the absorber near $x$ carries an $\alpha$-fraction of the Newtonian capacity of the ball of the same radius provides a local measure...

Yi-Qun Chen, Jie Xiao, Dachun Yang et al. · 0 citations

Preprint Aug 2026

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...

Yi-Qun Chen, Jie Xiao, Dachun Yang et al. · 0 citations