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

Vladimir Maz'ya·Alexander B. Movchan
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Abstract

Asymptotic formulae for Green's kernels $G_ε({\bf x}, {\bf y})$ 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 $ε\to 0$. 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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Vladimir Maz'ya, Alexander B. Movchan. 2006-06-27. Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains. https://arxiv.org/abs/math/0601753

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