2012/09/24 by Charles Z. Martin, Martin, Charles Z.
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Theoretical and Computational Physics #math-ph #math.AP #math.CV #math.MP #msc:31A10 #msc:35J08 #msc:35J10
paper · pdf · doi:10.48550/arxiv.1209.5363
arxiv created 2012/09/24 · arxiv updated 2012/09/25
We derive a variational formula for the outward normal derivative of the Green function for the Schrödinger 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.