Elliptic problems in domains with piecewise smooth boundaries. (English) Zbl 0806.35001

Nazarov, Sergey A.; Plamenevsky, Boris A.

De Gruyter Expositions in Mathematics. 13. Berlin: de Gruyter. vii, 525 p. (1994).

This book deals with elliptic boundary value problems in domains with nonregular boundary which may include conical points, edges or may be unbounded. The solvability of boundary value problems is studied and the asymptotic formulae for solutions near the singular points on the boundary are obtained. The authors present the general theory of elliptic boundary value problems in a cylinder and in a cone. Problems in domains with smooth edges and on manifolds with intersecting edges are considered. Radiation conditions are analyzed for boundary value problems in domains with outlets to infinity. Applications in solid mechanics and fracture phenomena are discussed.
The Russian original was published by Nauka (Moscow) in 1991.

Reviewer: A. Movchan (Bath)

MSC:

35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations
35J25	Boundary value problems for second-order elliptic equations
35C20	Asymptotic expansions of solutions to PDEs
74R99	Fracture and damage
35A20	Analyticity in context of PDEs
35B40	Asymptotic behavior of solutions to PDEs
35Jxx	Elliptic equations and elliptic systems
78A25	Electromagnetic theory (general)

Keywords:

radiation conditions; conical points; edges; singular points on the boundary