Open AccessLocal and nonlocal 1-Laplacian in Carnot groups
Author(s) -
Wojciech Górny
Publication year - 2022
Publication title -
annales fennici mathematici
Language(s) - English
Resource type - Journals
eISSN - 2737-114X
pISSN - 2737-0690
DOI - 10.54330/afm.114742
Subject(s) - carnot cycle , laplace operator , mathematics , euclidean geometry , operator (biology) , dirichlet problem , range (aeronautics) , dirichlet's energy , mathematical analysis , physics , geometry , boundary value problem , biochemistry , chemistry , materials science , repressor , gene , transcription factor , composite material , thermodynamics
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.