Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains
Vladimir Gilelevich Maz'ya, A. B. Movchan · Comptes Rendus Mathématique · 2006
Asymptotic formulae for Green's kernels G ε ( x , 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 → 0 . The main new feature of these asymptotic formulae is their uniformity with respect to the independent variables x and y .