Harmonic function

A function $f$ is called harmonic if it satisfies Laplace's equation:

Harmonic functions are important in many areas of mathematics and physics, including potential theory, electrostatics, fluid dynamics, and heat conduction. Examples include:

• The real and imaginary parts of a holomorphic function in complex analysis.
• The electrostatic potential in a charge-free region.
• The steady-state temperature distribution in a region with no heat sources.