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Partial Differential Equations and Complex Analysis

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Type.................: Ebook

Part Size............: 16,135,749 bytes









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Posted by............: ~tqw~



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Release Notes

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Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has

been a significant interaction between the theory of partial differential

equations and the function theory of several complex variables. Partial

Differential Equations and Complex Analysis explores the background and plumbs

the depths of this symbiosis.



The book is an excellent introduction to a variety of topics and presents many

of the basic elements of linear partial differential equations in the context of

how they are applied to the study of complex analysis. The author treats the

Dirichlet and Neumann problems for elliptic equations and the related Schauder

regularity theory, and examines how those results apply to the boundary

regularity of biholomorphic mappings. He studies the ?-Neumann problem, then

considers applications to the complex function theory of several variables and

to the Bergman projection.



Table Of Contents



Preface xi

1 The Dirichlet Problem in the Complex Plane 1

2 Review of Fourier Analysis 26

3 PseudodifferentialOperators 52

4 Elliptic Operators 76

5 Elliptic Boundary Value Problems 95

6 A Degenerate Elliptic Boundary Value Problem 128

7 The a-Neumann Problem 184

8 Applications of the a-Neumann Problem 252

9 The Local Solvability Issue and a Look Back 269

Table of Notation 283

Bibliography 287

Index 295



Product Details



* ISBN: 0849371554

* ISBN-13: 9780849371554

* Format: Hardcover, 320pp

* Publisher: CRC Press

* Pub. Date: July 1992

* Edition Number: 1



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