---
tag: 0DEB0JMN0W
kind: concept
name: Harmonic function
aliases: [solution-of-laplace-equation]
msc: [31B05]
uses: [0E0B6RA8K0]
sources:
  - url: https://en.wikipedia.org/wiki/Harmonic_function
    locator: lead section
same_as:
  wikidata: Q599027
  wikipedia: Harmonic function
---

## Summary

A harmonic function is a twice continuously differentiable function on an open subset of $\mathbb{R}^n$ whose [[Laplacian|0E0B6RA8K0]] is zero at each point.
Harmonic functions describe steady states, such as equilibrium temperatures and electrostatic potentials in empty space.