
Introduction  Table of Contents  Supplementary Material 
Mathematical Surveys and Monographs 2010; 608 pp; hardcover Volume: 162 ISBN10: 0821849832 ISBN13: 9780821849835 List Price: US$123 Member Price: US$98.40 Order Code: SURV/162 See also: Elliptic Boundary Value Problems in Domains with Point Singularities  V A Kozlov, V G Maz'ya and J Rossmann Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations  V A Kozlov, V G Maz'ya and J Rossmann  This is the first monograph which systematically treats elliptic boundary value problems in domains of polyhedral type. The authors mainly describe their own recent results focusing on the Dirichlet problem for linear strongly elliptic systems of arbitrary order, Neumann and mixed boundary value problems for second order systems, and on boundary value problems for the stationary Stokes and NavierStokes systems. A feature of the book is the systematic use of Green's matrices. Using estimates for the elements of these matrices, the authors obtain solvability and regularity theorems for the solutions in weighted and nonweighted Sobolev and Hölder spaces. Some classical problems of mathematical physics (Laplace and biharmonic equations, Lamé system) are considered as examples. Furthermore, the book contains maximum modulus estimates for the solutions and their derivatives. The exposition is selfcontained, and an introductory chapter provides background material on the theory of elliptic boundary value problems in domains with smooth boundaries and in domains with conical points. The book is destined for graduate students and researchers working in elliptic partial differential equations and applications. Readership Graduate students and research mathematicians interested in elliptic PDEs. Reviews "The book...is the third book in a series of books on the subject by these wellknown and prolific authors. [It] makes...welcome additions to the previous works of these authors. [The] results [are] useful in applications, such as...obtaining optimal rates of convergence of the finite element method."  Victor Nistor, Mathematical Reviews 


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