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AMS/IP Studies in Advanced Mathematics Partial Differential Equations in Several Complex VariablesOriginal Publication: 2001 Publisher: American Mathematical Society / International Press 
Description
This book is intended both as an introductory text and as a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the fields of CauchyRiemann and tangential CauchyRiemann operators. This book gives an uptodate account of the theories for these equations and their applications. The background material in several complex variables is developed in the first three chapters, leading to the Levi problem. The next three chapters are devoted to the solvability and regularity of the CauchyRiemann equations using Hilbert space techniques.The authors provide a systematic study of the CauchyRiemann equations and the $\bar\partial$Neumann problem, including $L^2$ existence theorems on pseudoconvex domains, $\frac 12$subelliptic estimates for the $\bar\partial$Neumann problems on strongly pseudoconvex domains, global regularity of $\bar\partial$ on more general pseudoconvex domains, boundary regularity of biholomorphic mappings, irregularity of the Bergman projection on worm domains. The second part of the book gives a comprehensive study of the tangential CauchyRiemann equations. Chapter 7 introduces the tangential CauchyRiemann complex and the Lewy equation. An extensive account of the $L^2$ theory for $\square_b$ and $\bar\partial_b$ is given in Chapters 8 and 9. Explicit integral solution representations are constructed both on the Heisenberg groups and on strictly convex boundaries with estimates in Ho$lder and $L^p$ spaces.Embeddability of abstract $CR$ structures is discussed in detail in the last chapter. This selfcontained book provides a muchneeded introductory text to several complex variables and partial differential equations. It is also a rich source of information to experts.
This volume is part of the AMS/IP Studies in Advanced Mathematics book series.
Publications
Pub. Date 
ISBN13 
ISBN10 
Medium 
Binding 
Size, Etc. 
Status 
List Price 

2019 Apr 
9781470438104 
EBook 
In Print 

2015 Jan 
9780821888230 
0821888234 
Out of Print 

2015 Jan 
9780821829615 
0821829610 
paperback 
Out of Print 

2001 
9780821810620 
0821810626 
Out of Print 