Partial Differential Equations and Complex Analysis / Edition 1

by Steven G. Krantz

Overview

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.

Product Details

ISBN-13:	9780367402754
Publisher:	Taylor & Francis
Publication date:	09/25/2019
Pages:	320
Product dimensions:	6.12(w) x 9.19(h) x (d)

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.

Editorial Reviews

Presents the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. Based on a year-long course at Washington University, requires a grounding in real and complex analysis; also helpful would be some acquaintance with measure theory, and a sophomore-level introductory course in differential equations. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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