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Advanced Mathematics for Applications by Andrea Prosperetti

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16

Green’s Functions: Partial Differential Equations

We have introduced the general idea of the Green’s function in §2.4 and we have presented some of the underlying theory in §15.6 and §15.7 of the previous chapter, which was mostly devoted to ordinary differential equations. Here we construct Green’s functions for partial differential equations. We will not repeat the theoretical considerations given earlier, but we will provide appropriate reference to that material.

16.1 Poisson equation

In all the cases treated in this chapter an essential ingredient for the construction of the adjoint operator and the identification of the concomitant (p. 391) is the divergence or Gauss theorem in d-dimensional space (see e.g. Kemmer 1977; Stroock ...

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