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Book review

Author(s) Grisvard, P.
Title Singularities in boundary value problem
Publisher Springer-Verlag
Year of publication 1992
Reviewed by Andrei Perjan

In this book the author examines the behaviour of the solutions of a boundary value problem for the stationary and non-stationary equations near corners, edges and vertices. He illustrates the technique of exposure of the singular term of solution, whose behavior is affected by the presence of non-smooth part of boundary on the model problems. As model problems are considered the boundary value problems for the Laplace equation, biharmonic equation, the elasticity system, the Stokes system with Dirichlet or Neumann conditions. The domains in which the boundary value problems are posed are strict polygons or polybedra. Also the wave and heat equations with Dirichlet conditions are investigated from the same point of view. All problems are posed in the sense of the Sobolev spaces. The available and possible generalizations and also the applications to the problems of exact controllability for the wave equation are indicated.

The book contains the scientific level information and should be bought by libraries. It can be helpful for the specialists in differential equations and control theory.