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

H. Benseridi, University Ferhat-Abbas, Setif, Algeria
M. Dilmi, University Med Boudiaf, M'sila, Algeria

E. J. Qualitative Theory of Diff. Equ., No. 13. (2010), pp. 1-12.

Abstract: 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.

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