# Poisson equation

A partial differential equation which is satisfied by the potential of a mass distribution inside domains occupied by the masses creating this potential. For the Newton potential in the space , , and the logarithmic potential in the Poisson equation has the form

where is the density of the mass distribution, is the area of the unit sphere in and is the value of the gamma-function.

Poisson's equation is a basic example of a non-homogeneous equation of elliptic type. The equation was first considered by S. Poisson (1812).

#### References

 [1] A.V. Bitsadze, "Equations of mathematical physics" , MIR (1980) (Translated from Russian) MR0587310 MR0581247 Zbl 0499.35002 [2] R. Courant, D. Hilbert, "Methods of mathematical physics. Partial differential equations" , 2 , Interscience (1965) (Translated from German) MR0195654