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Variational Formulas for the Green Function (1109.5386v2)
Published 25 Sep 2011 in math.CV, math-ph, math.AP, and math.MP
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, Schr\"odinger and Laplace--Beltrami.
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