Green's functions are mathematical constructs used to solve inhomogeneous differential equations, particularly in the context of boundary value problems. They provide a way to express the solution of a differential equation as an integral involving a source term and a kernel function, which encodes information about the domain and boundary conditions. This concept is vital for understanding the behavior of potentials, especially in solving Laplace's equation, exploring properties like the mean value property, handling Neumann boundary conditions, and relating to Riesz potentials.
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