Variation of Green Functions: Normal Derivatives
Complex Variables
2012-09-25 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We derive a variational formula for the outward normal derivative of the Green function for the Schr\"odinger and Laplace--Beltrami operators, viewed as perturbations of the Laplacian. As an application we begin to characterize elliptic growth---the growth of a domain pushed outward by its own Green function.
Cite
@article{arxiv.1209.5363,
title = {Variation of Green Functions: Normal Derivatives},
author = {Charles Z. Martin},
journal= {arXiv preprint arXiv:1209.5363},
year = {2012}
}