On the singular behavior of solutions of a transmission problem in a dihedral

摘要

In this paper, we study the singular behavior of solutions of a boundary value problem with mixed conditions in a neighborhood of an edge. The considered problem is defined in a nonhomogeneous body of $mathbb{R}^{3}$, this is done in the general framework of weighted Sobolev spaces. Using the results of Benseridi-Dilmi, Grisvard and Aksentian, we show that the study of solutions' singularities in the spatial case becomes a study of two problems: a problem of plane deformation and the other is of normal plane deformation.