Local and nonlocal 1-Laplacian in Carnot groups

Wojciech Górny

doi:10.54330/afm.114742

Local and nonlocal 1-Laplacian in Carnot groups

Författare

Wojciech Górny University of Warsaw, Faculty of Mathematics, Informatics and Mechanics

DOI: https://doi.org/10.54330/afm.114742

Nyckelord:

Random walk, least gradient functions, Carnot groups, nonlocal problems

Abstract

We formulate and study the nonlocal and local least gradient problem, which is the Dirichlet problem for the 1-Laplace operator, in the non-Euclidean 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. During this procedure, we prove a total variation estimate of independent interest and give an existence result for the local problem.