The Neumann Problem for the Cauchy-Riemann Complex. (AM-75), Volume 75 / / Joseph John Kohn, Gerald B. Folland.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Folland, Gerald B.,; Kohn, Joseph John,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2016]; ©1973
• Year of Publication: 2016
• Language: English
• Series: Annals of Mathematics Studies ; 75
• Physical Description: 1 online resource (156 p.)

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.

Table of Contents

Frontmatter -- FOREWORD -- TABLE OF CONTENTS -- CHAPTER I. FORMULATION OF THE PROBLEM -- CHAPTER II. THE MAIN THEOREM -- CHAPTER III. INTERPRETATION OF THE MAIN THEOREM -- CHAPTER IV. APPLICATIONS -- CHAPTER V. THE BOUNDARY COMPLEX -- CHAPTER VI. OTHER METHODS AND RESULTS -- APPENDIX: THE FUNCTIONAL ANALYSIS OF DIFFERENTIAL OPERATORS -- REFERENCES -- TERMINOLOGICAL INDEX -- TERMINOLOGICAL INDEX