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arXiv · 1912.00259

Asymptotic Mean Value Laplacian in Metric Measure Spaces

Andreas Minne·David Tewodrose
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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.

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Andreas Minne, David Tewodrose. 2019-11-30. Asymptotic Mean Value Laplacian in Metric Measure Spaces. https://arxiv.org/abs/1912.00259

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