**Green's Function For The Three-variable Laplace Equation**

In physics, the **Green's function (or fundamental solution) for Laplace's equation in three variables** is used to describe the response of a particular type of physical system to a point source. In particular, this Green's function arises in systems that can be described by Poisson's equation, a partial differential equation (PDE) of the form

where is the Laplace operator in, is the source term of the system, and is the solution to the equation. Because is a linear differential operator, the solution to a general system of this type can be written as an integral over a distribution of source given by :

where the Green's function for Laplace's equation in three variables describes the response of the system at the point to a point source located at :

and the point source is given by, the Dirac delta function.

Read more about Green's Function For The Three-variable Laplace Equation: Motivation, Mathematical Exposition, Rotationally Invariant Green's Functions For The Three-variable Laplace Equation

### Famous quotes containing the words green, function, laplace and/or equation:

“When the tea is brought at five o’clock,

And all the neat curtains are drawn with care,

The little black cat with bright *green* eyes

Is suddenly purring there.”

—Harold Monro (1879–1932)

“The information links are like nerves that pervade and help to animate the human organism. The sensors and monitors are analogous to the human senses that put us in touch with the world. Data bases correspond to memory; the information processors perform the *function* of human reasoning and comprehension. Once the postmodern infrastructure is reasonably integrated, it will greatly exceed human intelligence in reach, acuity, capacity, and precision.”

—Albert Borgman, U.S. educator, author. Crossing the Postmodern Divide, ch. 4, University of Chicago Press (1992)

“Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”

—Pierre Simon De *Laplace* (1749–1827)

“A nation fights well in proportion to the amount of men and materials it has. And the other *equation* is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”

—Norman Mailer (b. 1923)