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Complex Analytic Methods for Partial Differential Equations : An Introductory Text : An Introductory Text - Heinrich G W Begehr

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Complex Analytic Methods for Partial Differential Equations : An Introductory Text

An Introductory Text

By: Heinrich G W Begehr

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Hardcover | 1 December 1993

At a Glance

Hardcover
284 Pages

Dimensions(cm)
23.5 x 17.15 x 2.54

Hardcover

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This is an introductory text for beginners who have a basic knowledge in complex analysis, functional analysis and partial differential equations. The Riemann and Riemann-Hilbert boundary value problems are discussed for analytic functions, for generalized Cauchy-Riemann systems and for generalized Beltrami systems. Related problems, such as the Poincare problem, pseudoparabolic systems, half Dirichlet problems for the Dirac operator in Clifford analysis and elliptic second order equations are also considered. Estimates for solutions to linear equations existence and uniqueness results are thus available for related nonlinear problems; the method is explained by constructing entire solutions to nonlinear Beltrami equations.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Booktopia Publisher Services World Scientific Publishing Algebra

Preface
Function theoretical tools	p. 1
Cauchy integral	p. 1
Green functions and Schwarz operators	p. 18
Riemann boundary value problem	p. 38
Riemann-Hilbert boundary value problem	p. 45
Inhomogeneous Cauchy-Riemann systems	p. 69
Integral representations	p. 69
Properties of integral operators	p. 74
Boundary value problems for generalized Beltrami equations	p. 99
Generalized Beltrami equation	p. 99
Riemann boundary value problem	p. 114
Riemann-Hilbert boundary value problem	p. 118
Poincare boundary value problem	p. 144
Discontinuous boundary value problems	p. 149
Other equations and systems related to the Beltrami equation	p. 175
Initial boundary value problem for pseudoparabolic equations	p. 175
Initial boundary value problem for a composite type system	p. 184
Entire solution to nonlinear generalized Beltrami equations	p. 194
Higher order complex differential equations and equations in several complex variables	p. 203
Elliptic second order equations	p. 203
Higher order equations	p. 233
First order systems in two complex variables with analytic coefficients	p. 239
The Schwarz-Poisson formula for polydiscs	p. 252
References	p. 257
Index of Names	p. 267
Index of Subjects	p. 269
Index of Corollaries, Definitions, Lemmas, Theorems	p. 273
Table of Contents provided by Blackwell. All Rights Reserved.

Complex Analytic Methods for Partial Differential Equations : An Introductory Text

An Introductory Text

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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