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The Method of Layer Potentials for the Heat Equation in Time-Varying Domains : Memoirs of the American Mathematical Society - John L. Lewis

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

Memoirs of the American Mathematical Society

Paperback Published: January 1995
ISBN: 9780821803608
Number Of Pages: 157

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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 infinity results and discuss the Dirichlet and Neumann problems for a certain subclass of the domains.

Singular integrals
The David buildup scheme
Absolute continuity and Dirichlet-Neumann problems
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780821803608
ISBN-10: 0821803603
Series: Memoirs of the American Mathematical Society
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 157
Published: January 1995
Publisher: American Mathematical Society
Country of Publication: US
Dimensions (cm): 25.4 x 18.42  x 1.27
Weight (kg): 0.3

Earn 147 Qantas Points
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