Geodesic
Local and nonlocal 1-Laplacian in Carnot groups
Wojciech Górny1
1University of Warsaw, Faculty of Mathematics, Informatics and Mechanics
Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 427-456

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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.  
DOI : 10.54330/afm.114742
Keywords: Random walk, least gradient functions, Carnot groups, nonlocal problems

Wojciech Górny  1

1 University of Warsaw, Faculty of Mathematics, Informatics and Mechanics 
Wojciech Górny. Local and nonlocal 1-Laplacian in Carnot groups. Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 427-456. doi: 10.54330/afm.114742
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