Variational Formulas for the Green Function
Complex Variables
2011-10-26 v2 Mathematical Physics
Analysis of PDEs
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.
Cite
@article{arxiv.1109.5386,
title = {Variational Formulas for the Green Function},
author = {Charles Z. Martin},
journal= {arXiv preprint arXiv:1109.5386},
year = {2011}
}
Comments
12 pages