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- Title
The Neumann and Dirichlet problems for the total variation flow in metric measure spaces.
- Authors
Górny, Wojciech; Mazón, José M.
- Abstract
We study the Neumann and Dirichlet problems for the total variation flow in doubling metric measure spaces supporting a weak Poincaré inequality. We prove existence and uniqueness of weak solutions and study their asymptotic behavior. Furthermore, in the Neumann problem we provide a notion of solutions which is valid for L 1 initial data, as well as prove their existence and uniqueness. Our main tools are the first-order linear differential structure due to Gigli and a version of the Gauss–Green formula.
- Subjects
DIRICHLET problem; NEUMANN problem; METRIC spaces; NONSMOOTH optimization
- Publication
Advances in Calculus of Variations, 2024, Vol 17, Issue 1, p131
- ISSN
1864-8258
- Publication type
Article
- DOI
10.1515/acv-2021-0107