Published Paper
Inserted: 3 may 2023
Last Updated: 13 nov 2025
Journal: Journal of Mathematical Analysis and Applications
Volume: 491
Number: 2
Pages: 124330
Year: 2020
Abstract:
We use the mean value property in an asymptotic way to provide a notion of a pointwise Laplacian, called AMV Laplacian, that we study in several contexts including the Heisenberg group and weighted Lebesgue measures. We focus especially on a class of metric measure spaces including intersecting submanifolds of $\mathbb{R}^n$, a context in which our notion brings new insights; the Kirchhoff law appears as a special case. In the general case, we also prove a maximum and comparison principle, as well as a Green-type identity for a related operator.