Dirichlet and Neumann Problems for the Laplace Operator in Domains with Corners and Cone Vertices
Vladimir Gilelevich Maz'ya, С. А. Назаров, Boris A. Plamenevskij · Birkhäuser Basel eBooks · 2000
The purpose of the present chapter is twofold. On the one hand, we formulate and prove assertions required for constructing asymptotic expansions of solutions to boundary value problems involving the Laplace operator in domains with small variations of the boundary. On the other hand, this chapter illustrates the general theory of elliptic boundary value problems in domains with cone vertices, which is briefly presented in Chapter 3. (Therefore we refrain from using expansions by the eigenfunctions of the Beltrami operator, which lead to the same results in the case of the Poisson equation.) These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.