Variational Formulas for the Green Function

Details Variational Formulas for the Green Function Variational Formulas for the Green Function

2011-09-25

arxiv.org/abs/1109.5386v2

Mathematics

Complex Variables

12 pages

Scientific paper

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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