Extensions and traces of BV functions in rough domains and generalized Cheeger sets

Via the method of interior approximation, we prove trace and extension results for BV functions defined on a bounded domain omega C R-n such that omega satisfies Hn-1(& part;omega\omega(0)) < infinity , (0,1) where H(n-1 )is the (n - 1) dimensional Hausdorff measure and omega(0) is the measure-theoretic exterior of omega. Stronger results are obtained on a subclass of such domains, which are outward minimizing domains. We also obtain new weak regularity results for generalized Cheeger sets as byproducts.