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Elliptic Partial Differential Equations with Almost-Real Coefficients
 
Ariel Barton University of Minnesota, Minneapolis, MN
Elliptic Partial Differential Equations with Almost-Real Coefficients
Elliptic Partial Differential Equations with Almost-Real Coefficients
eBook ISBN:  978-0-8218-9875-8
Product Code:  MEMO/223/1051.E
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $43.20
Elliptic Partial Differential Equations with Almost-Real Coefficients
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Elliptic Partial Differential Equations with Almost-Real Coefficients
Elliptic Partial Differential Equations with Almost-Real Coefficients
Ariel Barton University of Minnesota, Minneapolis, MN
eBook ISBN:  978-0-8218-9875-8
Product Code:  MEMO/223/1051.E
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $43.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2232013; 106 pp
    MSC: Primary 35; Secondary 31;

    In this monograph the author investigates divergence-form elliptic partial differential equations in two-dimensional Lipschitz domains whose coefficient matrices have small (but possibly nonzero) imaginary parts and depend only on one of the two coordinates.

    He shows that for such operators, the Dirichlet problem with boundary data in \(L^q\) can be solved for \(q<\infty\) large enough. He also shows that the Neumann and regularity problems with boundary data in \(L^p\) can be solved for \(p>1\) small enough, and provide an endpoint result at \(p=1\).

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Definitions and the Main Theorem
    • 3. Useful Theorems
    • 4. The Fundamental Solution
    • 5. Properties of Layer Potentials
    • 6. Boundedness of Layer Potentials
    • 7. Invertibility of Layer Potentials and Other Properties
    • 8. Uniqueness of Solutions
    • 9. Boundary Data in \texorpdfstring{$H^1(\partial V)$}Hardy spaces
    • 10. Concluding Remarks
  • 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: 2232013; 106 pp
MSC: Primary 35; Secondary 31;

In this monograph the author investigates divergence-form elliptic partial differential equations in two-dimensional Lipschitz domains whose coefficient matrices have small (but possibly nonzero) imaginary parts and depend only on one of the two coordinates.

He shows that for such operators, the Dirichlet problem with boundary data in \(L^q\) can be solved for \(q<\infty\) large enough. He also shows that the Neumann and regularity problems with boundary data in \(L^p\) can be solved for \(p>1\) small enough, and provide an endpoint result at \(p=1\).

  • Chapters
  • 1. Introduction
  • 2. Definitions and the Main Theorem
  • 3. Useful Theorems
  • 4. The Fundamental Solution
  • 5. Properties of Layer Potentials
  • 6. Boundedness of Layer Potentials
  • 7. Invertibility of Layer Potentials and Other Properties
  • 8. Uniqueness of Solutions
  • 9. Boundary Data in \texorpdfstring{$H^1(\partial V)$}Hardy spaces
  • 10. Concluding Remarks
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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