Variational Formulas for the Green Function

2011/09/25 by Charles Z. Martin, Martin, Charles Z. · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #35J08 (Primary) 31A10 (Secondary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Electromagnetic Scattering and Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #math-ph #math.AP #math.CV #math.MP #msc:31A10 #msc:35J08

paper · pdf · doi:10.48550/arxiv.1109.5386

12 pages

openalex publication_date 2011/09/25 · arxiv created 2011/10/25 · arxiv updated 2011/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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