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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
Front Cover for The Method of Layer Potentials for the Heat Equation in Time-Varying Domains
Available Formats:
Electronic 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
Front Cover for The Method of Layer Potentials for the Heat Equation in Time-Varying Domains
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  • Front Cover for The Method of Layer Potentials for the Heat Equation in Time-Varying Domains
  • Back Cover for The Method of Layer Potentials for the Heat Equation in Time-Varying Domains
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
Available Formats:
Electronic 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
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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
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