Complex Methods for Partial Differential Equations

by Begehr, Heinrich G. W.; Celebi, A. Okay; Tutschke, Wolfgang

• ISBN13: 9780792360001
• ISBN10: 0792360001
• Format: Hardcover
• Copyright: 1999-12-01
• Publisher: Kluwer Academic Pub

Summary

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.

Table of Contents

Preface	ix
A reflection principle and its applications	1	(20)
J. Witte
On some problems for first order elliptic systems in the plane	21	(8)
D.Q. Dai
Differential--operator solutions for complex partial differential equations	29	(12)
O. Celebi
S. Sengul
On a generalized Riemann--Hilbert boundary value problem for second order elliptic systems in the plane	41	(16)
M. Akal
Boundary value problems of the theory of generalized analytic functions	57	(40)
G. Manjavidze
G. Akhalaia
On well--posedness of problems for nonclassical systems of equations	97	(6)
D. Kh. Safarov
An application of the periodic Riemann boundary value problem to a periodic crack problem	103	(10)
X. Li
Initial and boundary value problems for singular differential equations and applications to the theory of cusped bars and plates	113	(38)
G. Jaiani
Multidimensional logarithmic residues and their applications	151	(4)
L.A. Aizenberg
The Neumann problem for the inhomogeneous pluriharmonic system in polydiscs	155	(10)
A. Mohammed
Second order Cauchy--Pompeiu representations	165	(24)
H. Begehr
On a class of second order elliptic overdetermined systems	189	(16)
A. Dzhuraev
Boundary spinors and values of holomorphic functions	205	(10)
J. Cnops
Two approaches to non--commutative geometry	215	(30)
V.V. Kisil
Some partial differential equations in Clifford analysis	245	(18)
E. Obolashvili
Generalized monogenic functions satisfying differential equations with anti--monogenic right--hand sides	263	(8)
W. Tutschke
U. Yuksel
Complex analytic method for hyperbolic equations of second order	271	(18)
G.-C. Wen
Remarks on the solvability of Dirichlet problems in different function spaces	289	(6)
F. Rihawi
Complex methods in the theory of initial value problems	295	(18)
W. Tutschke
Optimal balls for solving fixed--point problems in Banach spaces	313	(6)
W. Tutschke
Wavelet transform of operators and functional calculus	319
V. V. Kisil