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.
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Martin, C.Z. Variational formulas for the Green function. Anal.Math.Phys. 2, 89–103 (2012). https://doi.org/10.1007/s13324-011-0015-0
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DOI: https://doi.org/10.1007/s13324-011-0015-0