Laplace Equation

★★★★☆Undergraduate

📖Definition

Elliptic PDE describing steady state. Defines harmonic functions

📐Formulas

∇²u = 0
∂²u/∂x² + ∂²u/∂y² = 0
Mean value property
Maximum principle

✏️Examples

예제 1

Electrostatic potential

예제 2

Steady heat conduction

예제 3

Fluid flow

Applications

Electromagnetism

Fluid mechanics

Gravity

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