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
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