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

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

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 Poincaré inequality. We show that solutions exist under certain regularity assumptions on the domain, but are generally...

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Bibliographic Details
Main Authors: Lahti Panu, Malý Lukáš, Shanmugalingam Nageswari
Format: Article
Language:English
Published: De Gruyter 2018-02-01
Series:Analysis and Geometry in Metric Spaces
Subjects:
bounded variation
metric measure space
neumann problem
positive mean curvature
stability
30l99
26b30
43a85
Online Access:https://doi.org/10.1515/agms-2018-0001

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