English

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

R2 v1 2026-06-23T13:05:18.035Z