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math.AP2021★ 1 cited
The Neumann and Dirichlet problems for the total variation flow in metric measure spaces
Wojciech Górny, José M. Mazón
We study the Neumann and Dirichlet problems for the total variation flow in metric measure spaces. We prove existence and uniqueness of weak solutions and study their asymptotic be…
math.AP2021
The Anzellotti-Gauss-Green formula and least gradient functions in metric measure spaces
Wojciech Górny, José M. Mazón
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…
math.AP2021
On the -Laplacian evolution equation in metric measure spaces
Wojciech Górny, José M. Mazón
The -Laplacian evolution equation in metric measure spaces has been studied as the gradient flow in of the -Cheeger energy (for ). In this paper, using…