Elliptic Equations in Polyhedral Domains (Mathematical Surveys and Monographs) by Vladimir Mazya and Jurgen Rossmann (PDF)

Description

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 Navier-Stokes 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 non-weighted Sobolev and Holder spaces. Some classical problems of mathematical physics (Laplace and biharmonic equations, Lame system) are considered as examples. Furthermore, the book contains maximum modulus estimates for the solutions and their derivatives. The exposition is self-contained, 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.

User’s Reviews

Editorial Reviews: Review “The book…is the third book in a series of books on the subject by these well-known 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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