---
tag: 0E0B6RA8K0
kind: concept
name: Laplacian
aliases: [laplace-operator]
msc: [35J05]
uses: [0MWV6ZTK6S, 0ABK9V9Y64]
sources:
  - url: https://en.wikipedia.org/wiki/Laplace_operator
    locator: Definition
same_as:
  wikidata: Q203484
  wikipedia: Laplace operator
---

## Summary

The Laplacian of a twice differentiable function on $\mathbb{R}^n$ is the [[divergence|0MWV6ZTK6S]] of its [[gradient|0ABK9V9Y64]].
It measures how the value of the function at a point differs from its average value on small spheres around the point.