Quaternionic Analysis and Elliptic Boundary Value Problems
General Material Designation
[Book]
First Statement of Responsibility
by Klaus Gürlebeck, Wolfgang Sprößig.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Basel :
Name of Publisher, Distributor, etc.
Birkhäuser Basel,
Date of Publication, Distribution, etc.
1989.
SERIES
Series Title
International Series of Numerical Mathematics/Internationale Schriftenreihe zur Numerischen Mathematik/Série internationale d'Analyse numérique ;
Volume Designation
89
CONTENTS NOTE
Text of Note
1. Quaternionic Analysis -- 1.1. Algebra of Real Quaternions -- 1.2. H-regular Functions -- 1.3. A Generalized LEIBNIZ Rule -- 1.4. BOREL-POMPEIU's Formula -- 1.5. Basic Statements of H-regular Functions -- 2. Operators -- 2.3. Properties of the T-Operator -- 2.4. VEKUA's Theorems -- 2.5. Some Integral Operators on the Manifold -- 3. Orthogonal Decomposition of the Space L2,H(G) -- 4. Some Boundary Value Problems of DIRICHLET's Type -- 4.1. LAPLACE Equation -- 4.2. HELMHOLTZ Equation -- 4.3. Equations of Linear Elasticity -- 4.4. Time-independent MAXWELL Equations -- 4.5. STOKES Equations -- 4.6. NAVIER-STOKES Equations -- 4.7. Stream Problems with Free Convection -- 4.8. Approximation of STOKES Equations by Boundary Value Problems of Linear Elasticity -- 5. H-regular Boundary Collocation Methods -- 5.1. Complete Systems of H-regular Functions -- 5.2. Numerical Properties of H-complete Systems of H-regular Functions -- 5.3. Foundation of a Collocation Method with H-regular Functions for Several Elliptic Boundary Value Problems -- 5.4. Numerical Examples -- 6. Discrete Quaternionic Function Theory -- 6.1. Fundamental Solutions of the Discrete Laplacian -- 6.2. Fundamental Solutions of a Discrete Generalized CAUCHY-RIEMANN Operator -- 6.3. Elements of a Discrete Quaternionic Function Theory -- 6.4. Main Properties of Discrete Operators -- 6.5. Numerical Solution of Boundary Value Problems of NAVIER-STOKES Equations -- 6.6. Concluding Remarks -- References -- Notations.