Pseudo-Differential Operators, Singularities, Applications

de Egorov, I͡U. V.

This book grew out of lecture notes based on the DMV seminar "Pseudo- Differential Operators, Singularities, Applications" held by the authors in Reisenburg-Günzburg, 12-19 July 1992. The modern theory of elliptic boundary value problems in domains having conical or edge singularities on the boundary as well as the classical theory of elliptic boundary value problems and the original Kondratiev theory are presented. This material forms the foundation for the second part of the book which contains a new construction of pseudo-differential operators with symbols corresponding to the singularities of the boundary of different dimensions. This allows in particular to obtain complete asymptotic expansions of solutions near these singularities.