Local and nonlocal 1-Laplacian in Carnot groups
Analysis of PDEs
2020-01-08 v1
Abstract
We formulate and study the nonlocal and local least gradient problem, which is the Dirichlet problem for the 1-Laplace operator, in a quite natural setting of Carnot groups. We study the passage from the nonlocal problem to the local problem as the range of the interaction goes to zero; to do this, we first prove a total variation estimate of independent interest.
Keywords
Cite
@article{arxiv.2001.02202,
title = {Local and nonlocal 1-Laplacian in Carnot groups},
author = {Wojciech Górny},
journal= {arXiv preprint arXiv:2001.02202},
year = {2020}
}
Comments
35 pages