On generalized divergence and Laplace operators as a matter of division of distributions
Volume 267 / 2022
Studia Mathematica 267 (2022), 261-294
MSC: Primary 35J05; Secondary 26A33, 46F12.
DOI: 10.4064/sm200625-29-1
Published online: 28 July 2022
Abstract
Motivated by the approach to the Laplacian on undirected weighted\break graphs, we provide a setting for a general point of view for a Kirchhoff type divergence and a Laplace operator built on the trivial gradient $f(y)-f(x)$ of order zero. We consider some particular classical and new instances of this approach and we introduce a notion of derivative as a tool for approximation of these operators.
