About: Green's function for the three-variable Laplace equation

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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 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.

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  • 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. (en)
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  • 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 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. (en)
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  • Green's function for the three-variable Laplace equation (en)
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