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Linear and Nonlinear Perturbations of the Operator $\operatorname{div}$
 
V. G. Osmolovskiĭ St. Petersburg State University, St. Petersburg, Russia
Linear and Nonlinear Perturbations of the Operator div
Hardcover ISBN:  978-0-8218-0586-2
Product Code:  MMONO/160
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4575-1
Product Code:  MMONO/160.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-0586-2
eBook: ISBN:  978-1-4704-4575-1
Product Code:  MMONO/160.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Linear and Nonlinear Perturbations of the Operator div
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Linear and Nonlinear Perturbations of the Operator $\operatorname{div}$
V. G. Osmolovskiĭ St. Petersburg State University, St. Petersburg, Russia
Hardcover ISBN:  978-0-8218-0586-2
Product Code:  MMONO/160
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4575-1
Product Code:  MMONO/160.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-0586-2
eBook ISBN:  978-1-4704-4575-1
Product Code:  MMONO/160.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 1601997; 104 pp
    MSC: Primary 35;

    The perturbation theory for the operator div is of particular interest in the study of boundary-value problems for the general nonlinear equation \(F(\dot y,y,x)=0\). Taking as linearization the first order operator \(Lu=C_{ij}u_{x_j}^i+C_iu^i\), one can, under certain conditions, regard the operator \(L\) as a compact perturbation of the operator div.

    This book presents results on boundary-value problems for \(L\) and the theory of nonlinear perturbations of \(L\). Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator \(L\). An analog of the Weyl decomposition is proved.

    The book also contains a local description of the set of all solutions (located in a small neighborhood of a known solution) to the boundary-value problems for the nonlinear equation \(F(\dot y, y, x) = 0\) for which \(L\) is a linearization. A classification of sets of all solutions to various boundary-value problems for the nonlinear equation \(F(\dot y, y, x) = 0\) is given.

    The results are illustrated by various applications in geometry, the calculus of variations, physics, and continuum mechanics.

    Readership

    Graduate students and research mathematicians interested in partial differential equations.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Linear perturbations of the operator div
    • Chapter 2. Nonlinear perturbations of the operator div
    • Appendix
  • 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: 1601997; 104 pp
MSC: Primary 35;

The perturbation theory for the operator div is of particular interest in the study of boundary-value problems for the general nonlinear equation \(F(\dot y,y,x)=0\). Taking as linearization the first order operator \(Lu=C_{ij}u_{x_j}^i+C_iu^i\), one can, under certain conditions, regard the operator \(L\) as a compact perturbation of the operator div.

This book presents results on boundary-value problems for \(L\) and the theory of nonlinear perturbations of \(L\). Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator \(L\). An analog of the Weyl decomposition is proved.

The book also contains a local description of the set of all solutions (located in a small neighborhood of a known solution) to the boundary-value problems for the nonlinear equation \(F(\dot y, y, x) = 0\) for which \(L\) is a linearization. A classification of sets of all solutions to various boundary-value problems for the nonlinear equation \(F(\dot y, y, x) = 0\) is given.

The results are illustrated by various applications in geometry, the calculus of variations, physics, and continuum mechanics.

Readership

Graduate students and research mathematicians interested in partial differential equations.

  • Chapters
  • Chapter 1. Linear perturbations of the operator div
  • Chapter 2. Nonlinear perturbations of the operator div
  • Appendix
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
Please select which format for which you are requesting permissions.