长期以来，复分析方法在偏微分方程方面的应用基本上局限于对线性与拟线性椭圆型方程和方程组的研究，而本书则把现代复分析方法扩充到对非线性椭圆型、抛物型、双曲型和混合型方程的研究，包括高维区域的一些情况，开拓了复分析研究的新领域。书中系统地介绍了作者在这方面所得的最新和最重要的复分析理论和方法，其中也包括把这些理论和方法用来解决非线性力学中一些边值问题的应用。

Preface

Chapter 1 Foundational Theorems of Nonlinear Quasiconformal Mappings

and Quasiconformal Shift Theorems

 1.1 Existence Theorems of Nonlinear Quasiconformal Mappings in

Multiply Connected Domains

 1.2 Uniqueness Theorems of Nonlinear Quasiconformal Mappings in

Multiply Connected Domains

 1.3 General Quasiconformal Shift Theorems in Multiply Connected Domains

 1.4 Quasiconformal Shift Theorems with Other Shift Conditions

Chapter 2 Boundary Value Problems for Nonlinear Elliptic Complex Equations and Systems

 2.1 Reduction of General Uniformly Elliptic Systems of First Order

Equations to standard Complex Form

 2.2 The Well-Posedness of Riemann-Hilbert Problem with Nonsmooth Boundary

 2.3 A Prior Estimate of Solutions for Problems B and B'

 2.4 Uniqueness of Solutions and Solvability for Problems B and B'

 2.5 Formulation of Oblique Derivative Problems of Second Order Systems

and Statement of Main Theorem

 2.6 Formulation of Modified Problem of First Order System and Integral

Expression of Its Solutions

 2.7 Estimates of Solutions for Modified Boundary Value Problem of First Order System

 2.8 Solvability of Modified Problem of First Order System and Oblique

Derivative Problem of Second Order System

Chapter 3 Discontinuous Boundary Value Problems for Analytic Functions

and Nonlinear Elliptic Equations

 3.1 General Discontinuous Boundary Value Problem for Analytic Functions

in Upper Half-Plane

 3.2 General Discontinuous Boundary Value Problem for Analytic Functions

in Unit-Disk

 3.3 Formulation of Discontinuous Irregular Oblique Derivative Problems

for Nonlinear Elliptic Equations

 3.4 Uniqueness and Estimates of Solutions of General Discontinuous Oblique

Derivative Problems

 3.5 Solvability of General Discontinuous Oblique Derivative Problems

 3.6 General Continuous Oblique Derivative Problems

Chapter 4 Approximate Methods for Solving Elliptic Systems and Their Error Estimate

 4.1 Newton Imbedding Method of Riemann-Hilbert Problem for Nonlinear Elliptic

Systems of First Order

 4.2 Error Estimates of Approximate Solutions of Riemann-Hilbert Problem for

Elliptic Systems of First Order

 4.3 Transformation of Elliptic Systems and Compound Boundary Value Problem

 4.4 Variation-Difference Method of Solving Compound Boundary Value Problem

 4.5 Variation-Difference Method of Oblique Derivative Problem for Second Order

Elliptic Equations

Chapter 5 Oblique Derivative Problems for Degenerate Equations of Mixed Type in

Multiply Connected Domains

 5.1 Formulation of Oblique Derivative Problem for Degenerate Equations of Mixed Type

 5.2 Representation of Solutions of Oblique Derivative Problem for Degenerate

Equations of Mixed Type

 5.3 Uniqueness of Solutions of Oblique Derivative Problem for Degenerate Equations of Mixed Type

 5.4 Solvability of Oblique Derivative Problem for Degenerate Hyperbolic Equations

 5.5 Solvability of Oblique Derivative Problem for Degenerate Elliptic Equations

and Equations of Mixed Type

 5.6 Frankl Type Problem for General Equations of Mixed Type in Multiply Connected Domains

Chapter 6 Applications of Complex Analysis and Inverse Problem for Planar Elliptic

Complex Equations

 6.1 Planar Filtration of Earth Dam with Nonhomogeneous Medium

 6.2 Planar Filtration Problems Associated with Nonhomogeneous and Anisotropic Medium

 6.3 Boundary Value Problems for Axisymmetric Filtration

 6.4 Two Free Boundary Problems in Planar Subsonic Steady Flow

 6.5 Formulation of Inverse Problem for Quasilinear Elliptic Complex Equations of

First Order

 6.6 Existence of Solutions of Inverse Problem for Elliptic Complex Equations of

First Order

 6.7 Global Uniqueness for Inverse Problem of Elliptic Complex Equations of First

Order

 6.8 Inverse Problem for Quasilinear Elliptic Equations of Second Order from

Dirichlet to Neumann Map

Chapter 7 Some Boundary Value Problems for Several Complex Variables and Clifford Analysis

 7.1 Riemann Boundary Value Problem for Analytic Fhnctions

 7.2 Riemann Problem of Inhomogeneous Cauchy-Riemann Systems

 7.3 Riemann-Hilbert Problem for Analytic Fhnctions in Polycylinder

 7.4 General Boundary Value Problem for Analytic Functions

 7.5 Oblique Derivative Problems for Generalized Regular Functions in R3

 7.6 Oblique Derivative Problem for Degenerate Elliptic System of First Order in R3

 7.7 Oblique Derivative Problem for Elliptic System of First Order in R4

Chapter 8 Nonlinear Parabolic and Elliptic Systems of Second Order in Higher Dimensional Domains

 8.1 Formulation of Initial-Irregular Oblique Derivative Problem for Nonlinear Parabolic Equations

 8.2 A Priori Estimates of Solutions of Initial-Oblique Derivative Problem

 8.3 Solvability of Initial-Oblique Derivative Problem

 8.4 Estimates and Existence of Solutions of Initial-Irregular Oblique Derivative Problems

 8.5 Formulation of Initial-Oblique Derivative Problems for Parabolic Systems in

High Dimensional Domains

 8.6 A Priori Estimates of Solutions for Initial-Oblique Derivative Problems for

Nonlinear Parabolic Systems

 8.7 Solvability of Initial-Oblique Derivative Problems for Nonlinear Parabolic Systems

 8.8 Oblique Derivative Problems for Nonlinear Elliptic Systems in High Dimensional Domains

References

Appendix Curriculum Vitae of WEN Guochun