Green's Function For The Three-variable Laplace Equation

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

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