Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
Small Modifications of Quadrature Domains
 
Makoto Sakai , Kawasaki, Japan
Front Cover for Small Modifications of Quadrature Domains
Available Formats:
Electronic ISBN: 978-1-4704-0583-0
Product Code: MEMO/206/969.E
List Price: $98.00
MAA Member Price: $88.20
AMS Member Price: $58.80
Front Cover for Small Modifications of Quadrature Domains
Click above image for expanded view
  • Front Cover for Small Modifications of Quadrature Domains
  • Back Cover for Small Modifications of Quadrature Domains
Small Modifications of Quadrature Domains
Makoto Sakai , Kawasaki, Japan
Available Formats:
Electronic ISBN:  978-1-4704-0583-0
Product Code:  MEMO/206/969.E
List Price: $98.00
MAA Member Price: $88.20
AMS Member Price: $58.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2062010; 269 pp
    MSC: Primary 31; Secondary 76;

    For a given plane domain, the author adds a constant multiple of the Dirac measure at a point in the domain and makes a new domain called a quadrature domain. The quadrature domain is characterized as a domain such that the integral of a harmonic and integrable function over the domain equals the integral of the function over the given domain plus the integral of the function with respect to the added measure. The family of quadrature domains can be modeled as the Hele-Shaw flow with a free-boundary problem. The given domain is regarded as the initial domain and the support point of the Dirac measure as the injection point of the flow.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction and Main Results
    • 2. Quadrature Domains
    • 3. Construction of Measures for Localization
    • 4. Generalizations of the Reflection Theorem
    • 5. Continuous Reflection Property and Smooth Boundary Points
    • 6. Proofs of (1) and (3) in Theorem 1.1
    • 7. Corners with Right Angles
    • 8. Properly Open Cusps
    • 9. Microlocalization and the Local-Reflection Theorem
    • 10. Modifications of Measures in $R^+$
    • 11. Modifications of Measures in $R^-$
    • 12. Sufficient Conditions for a Cusp to be a Laminar-Flow Point
    • 13. Turbulent-Flow Points
    • 14. The Set of Stationary Points
    • 15. Open Questions
  • Request Review Copy
  • Get Permissions
Volume: 2062010; 269 pp
MSC: Primary 31; Secondary 76;

For a given plane domain, the author adds a constant multiple of the Dirac measure at a point in the domain and makes a new domain called a quadrature domain. The quadrature domain is characterized as a domain such that the integral of a harmonic and integrable function over the domain equals the integral of the function over the given domain plus the integral of the function with respect to the added measure. The family of quadrature domains can be modeled as the Hele-Shaw flow with a free-boundary problem. The given domain is regarded as the initial domain and the support point of the Dirac measure as the injection point of the flow.

  • Chapters
  • 1. Introduction and Main Results
  • 2. Quadrature Domains
  • 3. Construction of Measures for Localization
  • 4. Generalizations of the Reflection Theorem
  • 5. Continuous Reflection Property and Smooth Boundary Points
  • 6. Proofs of (1) and (3) in Theorem 1.1
  • 7. Corners with Right Angles
  • 8. Properly Open Cusps
  • 9. Microlocalization and the Local-Reflection Theorem
  • 10. Modifications of Measures in $R^+$
  • 11. Modifications of Measures in $R^-$
  • 12. Sufficient Conditions for a Cusp to be a Laminar-Flow Point
  • 13. Turbulent-Flow Points
  • 14. The Set of Stationary Points
  • 15. Open Questions
Please select which format for which you are requesting permissions.