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

2021/05/02 by Wojciech Górny, Górny, Wojciech, José M. Mazón +1
Engineering · Mathematics · #26A45 #35J75 #49J52 #58J32 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2105.00432

openalex publication_date 2021/05/02 · openalex created_date 2023/05/13 · openalex updated_date 2026/07/28

Abstract

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

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