Quaternionic analysis and elliptic boundary value problems

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Inhaltsverzeichnis1. 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.