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What (who) is Green's function - definition

Green's function

$If one knows the solution <math display="inline">G(x,x')</math> to a differential equation subject to a point source <math display="inline">\hat{L}(x) G(x,x') = \delta(x-x')</math> and the differential operator <math display="inline">\hat{L}(x)</math> is linear, then one can superpose them to build the solution <math display="inline">u(x) = \int f(x') G(x,x') \, dx'</math> for a general source <math display="inline">\hat{L}(x) u(x) = f(x)</math>.$

GREEN'S FUNCTIONS

Greens function; Green's functions; Green’s function; Green's Functions; Green's Function

In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions.

https://en.wikipedia.org/wiki/Green's_function

Green's function number

In mathematical heat conduction, the Green's function number is used to uniquely categorize certain fundamental solutions of the heat equation to make existing solutions easier to identify, store, and retrieve.

https://en.wikipedia.org/wiki/Green's_function_number

Green's function for the three-variable Laplace equation

PARTIAL DIFFERENTIAL EQUATIONS

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

https://en.wikipedia.org/wiki/Green's_function_for_the_three-variable_Laplace_equation