Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains

Details Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains

2006-01-31

arxiv.org/abs/math/0601753v3

Mathematics

Analysis of PDEs

9 pages

Scientific paper

Asymptotic formulae for Green's kernels $G_\epsilon({\bf x}, {\bf y})$ of various boundary value problems for the Laplace operator are obtained in regularly perturbed domains and certain domains with small singular perturbations of the boundary, as $\epsilon \to 0$. The main new feature of these asymptotic formulae is their uniformity with respect to the independent variables ${\bf x}$ and ${\bf y}$.

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