Variation of Green's Functions

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Abstract
The variation of the Green's function of a linear differential operator is computed as the variation of an n-tuple integral with variable boundary. This generalization of Hadamard formula is shown to lead naturally to the method of ``invariant imbedding'' of R. Bellman. Three applications of the general formalism are given: the Dirichlet problem, the neutron or photon transport in a plane parallel anisotropically scattering slab, and scattering in a central field where three identities used in potential scattering are shown to be a consequence of the invariance of the asymptotic Green's function.

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