Complex Methods for Partial Differential Equations (International Society for Analysis, Applications and Computation)

Hardcover, x + 331 pages, NOT ex-library. A clean and bright copy with unmarked text and firm binding, free of inscriptions and stamps. Boards show small indentations. Published without a dust jacket. -- The book contains review chapters as well as state-of-the-art research chapters on topics ranging from complex elliptic first-order systems and second-order systems with regular or singular coefficients to overdetermined systems in several complex variables and partial differential equations in Clifford analysis. Different boundary value problems are studied. Applications to crack problems in elasticity theory to cusped bars, plates, and shells are given. Wavelet transformations are constructed in Banach spaces and used to identify complex analysis from the viewpoint of geometry. Fixed-point problems, even in abstract Banach spaces, are investigated with respect to an optimal domain of existence for the solution. Audience: Researchers working in the field as well as scientists interested in the applications. -- Contents: A Reflection Principle and Its Applications; On Some Problems for First Order Elliptic Systems in the Plane; Differential-operator Solutions for Complex Partial Differential Equations; On a Generalized Riemann-Hilbert Boundary Value Problem for Second Order Elliptic Systems in the Plane; Boundary Value Problems of the Theory of Generalized Analytic Functions; On Well-Posedness of Problems for Nonclassical Systems of Equations; An Application of the Periodic Riemann Boundary Value Problem to a Periodic Crack Problem; Initial and Boundary Value Problems for Singular Differential Equations and Applications to the Theory of Cusped Bars and Plates; Multidimensional Logarithmic Residues and Their Applications; Neumann Problem for the Inhomogeneous Pluriharmonic System in Polydiscs; Second Order Cauchy-Pompeiu Representations; On a Class of Second Order Elliptic Overdetermined Systems; Boundary Spinors and Values of Holomorphic Functions; Two Approaches to Non-commutative Geometry; Some Partial Differential Equations in Clifford Analysis; Generalized Monogenic Functions Satisfying Differential Equations with Anti-Monogenic Right-Hand Sides; Complex Analytic Method for Hyperbolic Equations of Second Order; Remarks on the Solvability of Dirichlet Problems in Different Function Spaces; Complex Methods in the Theory of Initial Value Problems; Optimal Balls for Solving Fixed-Point Problems in Banach Spaces; Wavelet Transform of Operators and Functional Calculus.