Poisson equation

The partial differential equation

where ∇² is the Laplacian operator, φ a scalar function of position, and F a given function of the independent space variables.
For the special case F = 0, the Poisson equation reduces to the Laplace equation.
See relaxation method.

The relationship between temperature T and pressure p of an ideal gas undergoing an adiabatic process; given by

where T₀ and p₀ are initial state values and κ is the Poisson constant. With p₀ given as a reference pressure of 100 kPa, T₀ is equal to the potential temperature.