Behavior of solutions of the Neumann problem for the Poisson equation near straight edges (Q2344903)

In this article, the Neumann problem for the Poisson equation in a domain \(\mathcal{D}=K\times \mathbb{R}^{n-m}\) with \(K\) a cone in \(\mathbb{R}^m\) is considered. First, the author deals with the singularities of the Green function close to the edges of the given domain. Next, he uses the decomposition of the Green function to obtain asymptotics of the solution of the boundary value problem under the assumption that the right-hand side function belongs to a weighted \(L_p\) Sobolev space. The author provides precise formulas for all coefficients in the asymptotics.