Asymptotic Behaviour of Energy Integrals for Small Perturbations of the Boundary Near Corners and Isolated Points
Vladimir Gilelevich Maz'ya, С. А. Назаров, Boris A. Plamenevskij · Birkhäuser Basel eBooks · 2000
This chapter deals with boundary value problems in domains perturbed near conic vertices or isolated points. In the first case the perturbation results in smoothing of the boundary in a neighborhood of the singularity, and in the second case the isolated point is transformed into a small hole. Our aim is to derive and to justify mathematically asymptotic formulas for energy functionals applied to boundary value problems for systems which are elliptic in the sense of Douglis-Nirenberg.