Laplace equation

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Laplace equation

The elliptic partial differential equation
ams2001glos-Le3
where φ is a scalar function of position, and ∇2 is the Laplacian operator.

In rectangular Cartesian coordinates x, y, z, this equation may be written
ams2001glos-Le4
The Laplace equation is satisfied, for example, by the velocity potential in an irrotational flow, by gravitational potential in free space, by electrostatic potential in the steady flow of electric currents in solid conductors, and by the steady-state temperature distribution in solids. A solution of the Laplace equation is called an harmonic function.
Compare Poisson equation.

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