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

Yiqun Chen, Jie Xiao, Dachun Yang +2

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 abs…