Variation of Green Functions: Normal Derivatives
  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. 
Charles Z. Martin
math.CV math-ph math.AP math.MP