Singular Partial Differential Equations: 1st Edition (Hardback) book cover

Singular Partial Differential Equations

1st Edition

By Abduhamid Dzhuraev

Chapman and Hall/CRC

216 pages

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Hardback: 9781584881445
pub: 1999-11-29
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Description

Singular Partial Differential Equations provides an analytical, constructive, and elementary approach to non-elementary problems. In the first monograph to consider such equations, the author investigates the solvability of partial differential equations and systems in a class of bounded functions with complex coefficients having singularities at the inner points or boundary of the domain.

Using complex variable techniques, the author considers a variety of problems, including the Dirichlet, Neumann, and other problems for first order systems. He also explores applications to singular equations, degenerate, high-dimensional Beltrami systems in Cn,, and others.

Singular Partial Differential Equations fills a gap in the literature on degenerate and singular partial differential equations and significantly contributes to the theory of boundary value problems for these equations and systems. It will undoubtedly stimulate further research in the field. Practical applications in analysis and physics make this important reading for researchers and students in physics and engineering, along with mathematicians.

Table of Contents

INTRODUCTION

FIRST ORDER ELLIPTIC SYSTEMS

General First Order Elliptic Systems in the Plane

First Order Elliptic Systems for a Single Function in the Complex Space

First Order Elliptic Systems for several functions in the Complex Space

The Riemann-Hilbert Problem for First Order Elliptic Systems in the Plane

The Riemann-Hilbert Problem for Systems in the Unit Ball of Cn

SECOND ORDER OF ELLIPTIC SYSTEMS

Second Order Elliptic Systems in the Plane

Second Order Elliptic Systems in Cn

Boundary Value Problems for Overdetermined Systems in the Unit Ball of Cn.

Some Second Order Elliptic Systems with Two Unknown Functions in C2

DEGENERATE AND SINGULAR ELLIPTIC SYSTEMS

Solvability of First Order Systems in the Plane

Solvability of First Order Overdetermined Systems in C2

SECOND ORDER ELLIPTIC SYSTEMS

Solvability of the Second Order Singular Elliptic Equations in the Unit Disc

Solvability of the Second Order Overdetermined Elliptic Systems of in the Unit Ball of Cn

Solvability of Elliptic Systems having Singularity at Infinity

Solvability of some Non-Elliptic Systems

BOUNDARY VALUE PROBLEMS FOR SINGULAR ELLIPTIC SYSTEMS

Boundary Value Problems for Singular Elliptic Systems in the Plane Domains

Boundary Value Problems for Singular Elliptic Systems in the Unit Ball of Cn

Boundary Value Problems for Equations having Pointwise Singularity

Some Nonlinear Problems

BIBLIOGRAPHY

INDEX

About the Series

Monographs and Surveys in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT007000
MATHEMATICS / Differential Equations
SCI040000
SCIENCE / Mathematical Physics