The Anzellotti-Gauss-Green formula and least gradient functions in metric measure spaces

Abstract

In the framework of the first-order differential structure introduced by Gigli, we obtain a Gauss-Green formula on regular bounded open sets of metric measure spaces, valid for BV functions and vector fields with integrable divergence. Then, we study least gradient functions in metric measure spaces using this formula as the main tool.

41 pages. arXiv admin note: text overlap with arXiv:2103.13373