Abstract
This chapter discusses the application of Green's function for the Laplace operator. It examines Green's function for various problems connected with Poisson's equation. The Laplace operator is self-adjoint. The homogeneous conditions corresponding to it are also self-adjoint. When one tries to solve the Neumann problem, either in space or in a plane, one meets a difficulty that Green's function does not exist as the corresponding homogeneous problem has a non-trivial solution, viz., a constant. A generalized Green's function is required to satisfy not Laplace's equation but the equation 2G (P, P0) = C. The chapter also explains this question in more detail.
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