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Elliptic Equations in Polyhedral Domains
 
Vladimir Maz′ya Linköping University, Linköping, Sweden
Jürgen Rossmann Rostock University, Rostock, Germany
Elliptic Equations in Polyhedral Domains
Hardcover ISBN:  978-0-8218-4983-5
Product Code:  SURV/162
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1389-7
Product Code:  SURV/162.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4983-5
eBook: ISBN:  978-1-4704-1389-7
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
Elliptic Equations in Polyhedral Domains
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Elliptic Equations in Polyhedral Domains
Vladimir Maz′ya Linköping University, Linköping, Sweden
Jürgen Rossmann Rostock University, Rostock, Germany
Hardcover ISBN:  978-0-8218-4983-5
Product Code:  SURV/162
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1389-7
Product Code:  SURV/162.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4983-5
eBook ISBN:  978-1-4704-1389-7
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 Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1622010; 608 pp
    MSC: 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 non-weighted 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 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.

    Readership

    Graduate 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 Miranda-Agmon 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 Navier-Stokes 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 Navier-Stokes systems in a bounded domain of polyhedral type
  • Reviews
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1622010; 608 pp
MSC: 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 non-weighted 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 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.

Readership

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 Miranda-Agmon 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 Navier-Stokes 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 Navier-Stokes systems in a bounded domain of polyhedral type
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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