arXiv Analytics

Sign in

arXiv:2001.02202 [math.AP]AbstractReferencesReviewsResources

Local and nonlocal 1-Laplacian in Carnot groups

Wojciech Górny

Published 2020-01-07Version 1

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.

Comments: 35 pages
Categories: math.AP
Subjects: 35R03, 49J45, 49K20, 49Q05
Related articles: Most relevant | Search more
arXiv:2204.13073 [math.AP] (Published 2022-04-27)
A note on monotonicity and Bochner formulas in Carnot groups
arXiv:1610.03270 [math.AP] (Published 2016-10-11)
Schauder estimates at the boundary for sub-laplacians in Carnot groups
arXiv:2401.07679 [math.AP] (Published 2024-01-15)
Some counterexamples to Alt-Caffarelli-Friedman monotonicity formulas in Carnot groups

Links

Toolbox