Approximation of BV by SBV functions in metric spaces

摘要

In a complete metric space that is equipped with a doubling measure and supports a Poincare inequality, we show that functions of bounded variation (BV functions) can be approximated in the strict sense and pointwise uniformly by special functions of bounded variation, without adding significant jumps. As a main tool, we study the variational 1-capacity and its BV analog. (C) 2020 Elsevier Inc. All rights reserved.