Variational Formulas for the Green Function
arXiv:1109.5386
Abstract
The Green function has a complex dependence upon its underlying domain and differential operator. We briefly review Hadamard's formula for the first variation of the Green function due to a perturbation of the domain. We then take a different avenue and approximate the change in the Green function when the Laplacian is perturbed into a number of different operators: Helmholtz, Schrödinger and Laplace--Beltrami.
12 pages