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

Maz'ya, Vladimir; Movchan, Alexander B.

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

Authors

Description

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 ${\bf y}$.
9 pages