Uniform estimates for polyharmonic Green functions in domains with small   holes
  We prove a pointwise control for the Green's function of polyharmonic operators with holes: this control is uniform while holes shrink. For the usual Laplacian, such a control is given by the maximum principle; the techniques developed here applies to general polyharmonic operators for which there is no comparison principle. 
Hans-Christoph Grunau and Fr\'ed\'eric Robert
math.AP