Unavoidable collections of balls for censored stable processes

Abstract

We study avoidability of collections of balls in bounded $C^{1,1}$ opens sets for censored $\alpha$-stable processes, $\alpha \in (1,2)$. The results are analog to the ones obtained for Brownian motion in S. J. Gardiner, M. Ghergu, Champagne subregions of the unit ball with unavoidable bubbles, Ann. Acad. Sci. Fenn. Math. 35 (2010) 321-329. On the way we derive a Wiener-Aikawa-type criterion for minimal thinness with respect to the censored stable processes.