An Analog of the Neumann Problem for the $1$-Laplace Equation in the Metric Setting: Existence, Boundary Regularity, and Stability

Panu Lahti, Lukas Maly, Nageswari Shanmugalingam

We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a…