2019/11/30 by Minne, Andreas, Tewodrose, David
#26B15 (Secondary) #28E99 #31C05 (Primary) #35B50 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.1912.00259
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 ℝn, 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.