Uniform estimates for polyharmonic Green functions in domains with small holes

2012/10/08 by Hans-Christoph Grunau, Grunau, Hans-Christoph, Frédéric Robert +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1210.2248

arxiv created 2012/10/08 · openalex publication_date 2012/10/08 · arxiv updated 2012/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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• Perturbed eigenvalues of polyharmonic operators in domains with small holes
• Uniform asymptotic formulae for Green's functions in singularly perturbed domains
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