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The Neumann Problem for the Cauchy-Riemann Complex by Gerald B. Folland, Joseph John Kohn

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About this book :-
The Neumann Problem for the Cauchy-Riemann Complex written by Gerald B. Folland, Joseph John Kohn
This book is based on the notes from lectures given by the second author at Princeton University in the year 1970-71, which were subsequently expanded and revised by the first author. Our aim has been to provide a thorough and coherent account of the solution of the J-Neumann problem and certain of its applications and ramifications, and we have taken the opportunity afforded by the monograph format to employ a somewhat more leisurely style than is common in the original journal articles. It is our hope that this book may thereby be accessible to a fairly wide audience and that it may also provide a sort of working introduction to some of the recent techniques in partial differential equations.
Part explanation of important recent work, and part introduction to some of the techniques of modern partial differential equations, this monograph is a self-contained exposition of the Neumann problem for the Cauchy-Riemann complex and certain of its applications. The authors prove the main existence and regularity theorems in detail, assuming only a knowledge of the basic theory of differentiable manifolds and operators on Hilbert space. They discuss applications to the theory of several complex variables, examine the associated complex on the boundary, and outline other techniques relevant to these problems. In an appendix they develop the functional analysis of differential operators in terms of Sobolev spaces, to the extent it is required for the monograph.
(Gerald B. Folland)

Book Detail :-
Title: The Neumann Problem for the Cauchy-Riemann Complex
Edition:
Author(s): Gerald B. Folland, Joseph John Kohn
Publisher: Princeton University Press
Series: Annals of Mathematics Studies 75
Year: 1972
Pages: 158
Type: PDF
Language: English
ISBN: 0691081204,9780691081205
Country: US
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About Author :-
Author Gerald Budge Folland is an American mathematician and a professor of mathematics at the University of Washington. His areas of interest are harmonic analysis (on both Euclidean space and Lie groups), differential equations, and mathematical physics. The title of his doctoral dissertation at Princeton University (1971) is "The Tangential Cauchy-Riemann Complex on Spheres".
He is the author of several textbooks in mathematical analysis. In 2012 he became a fellow of the American Mathematical Society.

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Book Contents :-
The Neumann Problem for the Cauchy-Riemann Complex written by Gerald B. Folland cover the following topics.
1. Formulation of the Problem
2. The Main Theorem
3. Interpretation of the Main Theorem
4. Applications
5. The Boundary Complex
6. Other Methods and Results
Appendix The Functional Analysis of Differential Operators
Refrences
Terminological Index
Notational Index


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