The method of layer potentials for the heat equation in time-varying domains
著者
書誌事項
The method of layer potentials for the heat equation in time-varying domains
（Memoirs of the American Mathematical Society, no. 545）
American Mathematical Society, 1995
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注記
"March 1995, Volume 114, number 545 (first of 4 numbers)" -- T.p
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
Singular integrals The David buildup scheme Absolute continuity and Dirichlet-Neumann problems.
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