Open AccessUniform estimates for polyharmonic Green functions in domains with small holes
Author(s) -
Hans-Christoph Grunau,
Frédéric Robert
Publication year - 2013
Publication title -
contemporary mathematics - american mathematical society
Language(s) - English
Resource type - Reports
SCImago Journal Rank - 0.106
H-Index - 12
eISSN - 1098-3627
pISSN - 0271-4132
DOI - 10.1090/conm/595/11811
Subject(s) - pointwise , mathematics , polyharmonic spline , green s , function (biology) , control (management) , mathematical analysis , mathematical optimization , pure mathematics , computer science , artificial intelligence , nearest neighbor interpolation , linear interpolation , polynomial , evolutionary biology , biology
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.
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