**Memoirs of the American Mathematical Society**

1995;
157 pp;
Softcover

MSC: Primary 42; 35;

Print ISBN: 978-0-8218-0360-8

Product Code: MEMO/114/545

List Price: $47.00

Individual Member Price: $28.20

**Electronic ISBN: 978-1-4704-0124-5
Product Code: MEMO/114/545.E**

List Price: $47.00

Individual Member Price: $28.20

# The Method of Layer Potentials for the Heat Equation in Time-Varying Domains

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*John L. Lewis; Margaret A. M. Murray*

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.

#### Table of Contents

# Table of Contents

## The Method of Layer Potentials for the Heat Equation in Time-Varying Domains

#### Readership

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