Fractional Sobolev norms and BV functions on manifolds. (October 2019) - Kreuml, Andreas; Mordhorst, Olaf
Abstract: The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on compact manifolds. As an application the special case of sets of finite perimeter is considered.