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Hardcover ISBN:  9780821849835 
Product Code:  SURV/162 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413897 
Product Code:  SURV/162.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821849835 
eBook ISBN:  9781470413897 
Product Code:  SURV/162.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 162; 2010; 608 ppMSC: Primary 35
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 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.
ReadershipGraduate students and research mathematicians interested in elliptic PDEs.

Table of Contents

Chapters

1. Introduction

The Dirichlet problem for strongly elliptic systems in polyhedral domains

2. Prerequisites on elliptic boundary value problems in domains with conical points

3. The Dirichlet problem for strongly elliptic systems in a dihedron

4. The Dirichlet problem for strongly elliptic systems in a cone with edges

5. The Dirichlet problem in a bounded domain of polyhedral type

6. The MirandaAgmon maximum principle

Neumann and mixed boundary value problems for second order systems in polyhedral domains

7. Boundary value problems for second order systems in a dihedron

8. Boundary value problems for second order systems in a polyhedral cone

9. Boundary value problems for second order systems in a bounded polyhedral domain

Mixed boundary value problems for stationary Stokes and NavierStokes systems in polyhedral domains

10. Boundary value problem for the Stokes system in a dihedron

11. Mixed boundary value problems for the Stokes system in a polyhedral cone

12. Mixed boundary value problems for the Stokes and NavierStokes systems in a bounded domain of polyhedral type


Additional Material

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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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 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.
Graduate students and research mathematicians interested in elliptic PDEs.

Chapters

1. Introduction

The Dirichlet problem for strongly elliptic systems in polyhedral domains

2. Prerequisites on elliptic boundary value problems in domains with conical points

3. The Dirichlet problem for strongly elliptic systems in a dihedron

4. The Dirichlet problem for strongly elliptic systems in a cone with edges

5. The Dirichlet problem in a bounded domain of polyhedral type

6. The MirandaAgmon maximum principle

Neumann and mixed boundary value problems for second order systems in polyhedral domains

7. Boundary value problems for second order systems in a dihedron

8. Boundary value problems for second order systems in a polyhedral cone

9. Boundary value problems for second order systems in a bounded polyhedral domain

Mixed boundary value problems for stationary Stokes and NavierStokes systems in polyhedral domains

10. Boundary value problem for the Stokes system in a dihedron

11. Mixed boundary value problems for the Stokes system in a polyhedral cone

12. Mixed boundary value problems for the Stokes and NavierStokes systems in a bounded domain of polyhedral type

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