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
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
The Method of Layer Potentials for the Heat Equation in Time-Varying Domains
 
John L. Lewis University of Kentucky
Margaret A. M. Murray Virginia Polytech Institute & State University
The Method of Layer Potentials for the Heat Equation in Time-Varying Domains
eBook ISBN:  978-1-4704-0124-5
Product Code:  MEMO/114/545.E
List Price: $47.00
MAA Member Price: $42.30
AMS Member Price: $28.20
The Method of Layer Potentials for the Heat Equation in Time-Varying Domains
Click above image for expanded view
The Method of Layer Potentials for the Heat Equation in Time-Varying Domains
John L. Lewis University of Kentucky
Margaret A. M. Murray Virginia Polytech Institute & State University
eBook ISBN:  978-1-4704-0124-5
Product Code:  MEMO/114/545.E
List Price: $47.00
MAA Member Price: $42.30
AMS Member Price: $28.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1141995; 157 pp
    MSC: Primary 42; 35;

    Recent years have seen renewed interest in the solution of parabolic boundary value problems by the method of layer potentials, a method that has been extraordinarily useful in the solution of elliptic problems. This book develops this method for the heat equation in time-varying domains. In the first chapter, Lewis and Murray show that certain singular integral operators on \(L^p\) are bounded. In the second chapter, they develop a modification of the David buildup scheme, as well as some extension theorems, to obtain \(L^p\) boundedness of the double layer heat potential on the boundary of the domains. The third chapter uses the results of the first two, along with a buildup scheme, to show the mutual absolute continuity of parabolic measure and a certain projective Lebesgue measure. Lewis and Murray also obtain \(A_\infty\) results and discuss the Dirichlet and Neumann problems for a certain subclass of the domains.

    Readership

    Researchers and graduate students studying harmonic analysis and partial differential equations.

  • Table of Contents
     
     
    • Chapters
    • I. Singular integrals
    • II. The David buildup scheme
    • III. Absolute continuity and Dirichlet-Neumann problems
  • 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: 1141995; 157 pp
MSC: Primary 42; 35;

Recent years have seen renewed interest in the solution of parabolic boundary value problems by the method of layer potentials, a method that has been extraordinarily useful in the solution of elliptic problems. This book develops this method for the heat equation in time-varying domains. In the first chapter, Lewis and Murray show that certain singular integral operators on \(L^p\) are bounded. In the second chapter, they develop a modification of the David buildup scheme, as well as some extension theorems, to obtain \(L^p\) boundedness of the double layer heat potential on the boundary of the domains. The third chapter uses the results of the first two, along with a buildup scheme, to show the mutual absolute continuity of parabolic measure and a certain projective Lebesgue measure. Lewis and Murray also obtain \(A_\infty\) results and discuss the Dirichlet and Neumann problems for a certain subclass of the domains.

Readership

Researchers and graduate students studying harmonic analysis and partial differential equations.

  • Chapters
  • I. Singular integrals
  • II. The David buildup scheme
  • III. Absolute continuity and Dirichlet-Neumann problems
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.