Least gradient functions in metric random walk spaces

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 (N). Assuming that a Poincare inequality is satisfied, we study the Euler-Lagrange equation associated with the least gradient problem. We also prove the Poincare inequality in a few settings.

Automated summary

This paper investigates least gradient functions in metric random walk spaces, including those on locally finite weighted connected graphs and nonlocal least gradient functions on (N) as special cases. Assuming the satisfaction of a Poincare inequality, the Euler-Lagrange equation associated with the least gradient problem is studied. Additionally, the Poincare inequality is proven in various settings.