Volume 27, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Number of page(s)||32|
|Published online||01 March 2021|
Least gradient functions in metric random walk spaces
Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2,
2 Departamento de Anàlisis Matemàtico, Universitat de València, Dr. Moliner 50, 46100 Burjassot, Spain.
* Corresponding author: firstname.lastname@example.org
Accepted: 30 November 2020
In this paper we study least gradient functions in metric random walk spaces, which include as particular cases the least gradient functions on locally finite weighted connected graphs and nonlocal least gradient functions on ℝN. Assuming that a Poincaré inequality is satisfied, we study the Euler-Lagrange equation associated with the least gradient problem. We also prove the Poincaré inequality in a few settings.
Mathematics Subject Classification: 05C81 / 35R02 / 26A45 / 05C21 / 45C99
Key words: Random walk / least gradient functions / total variation flow / functions of bounded variation
© EDP Sciences, SMAI 2021
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