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The Anzellotti–Gauss–Green formula and least gradient functions in metric measure spaces.
- Source :
-
Communications in Contemporary Mathematics . Aug2024, Vol. 26 Issue 6, p1-42. 42p. - Publication Year :
- 2024
-
Abstract
- In the framework of the first-order differential structure introduced by Gigli, we obtain a Gauss–Green formula on regular bounded open sets in doubling metric measure spaces supporting a weak Poincaré inequality, valid for BV functions and vector fields with integrable divergence. Then, we study least gradient functions in metric measure spaces and provide an Euler–Lagrange-type formulation of the least gradient problem, using this formula as the main tool. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02191997
- Volume :
- 26
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Communications in Contemporary Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 177326651
- Full Text :
- https://doi.org/10.1142/S021919972350027X