Nazarov, Sergey A.; Plamenevsky, Boris A. Elliptic problems in domains with piecewise smooth boundaries. (English) Zbl 0806.35001 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) Cited in 2 ReviewsCited in 276 Documents 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 PDF BibTeX XML Cite \textit{S. A. Nazarov} and \textit{B. A. Plamenevsky}, Elliptic problems in domains with piecewise smooth boundaries. Berlin: de Gruyter (1994; Zbl 0806.35001)