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

Asymptotic formulae for Green's kernels $G_{\epsilon }(\mathbf{x},\mathbf{y})$ 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 x and y. To cite this article: V. Maz'ya, A. Movchan, C. R. Acad. Sci. Paris, Ser. I 343 (2006).