Partial Differential Equations and Complex Analysis: 1st Edition (Paperback) book cover

Partial Differential Equations and Complex Analysis

1st Edition

By Steven G. Krantz

CRC Press

320 pages

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Paperback: 9780367402754
pub: 2019-09-25
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Description

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

The Dirichlet Problem in the Complex Plane Review of Fourier Analysis Pseudodifferential Operators Elliptic Operators Elliptic Boundary Value Problems A Degenerate Elliptic Boundary Value Problem The ?- Neumann Problem Applications of the ?- Neumann Problem The Local Solvability Issue and a Look Back.

About the Author

Krantz, Steven G.

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT007000
MATHEMATICS / Differential Equations
MAT037000
MATHEMATICS / Functional Analysis