Quaternionic Analysis and Elliptic Bound
✍ K. Gürlebeck; W. Sprößig
📂 Library
📅 1990
🏛 De Gruyter
🌐 German
✦ LIBER ✦
📁
Quaternionic Analysis and Elliptic Boundary Value Problems
✍ Scribed by Klaus Gürlebeck, Wolfgang Sprößig (auth.)
- Publisher
- Birkhäuser Basel
- Year
- 1989
- Tongue
- English
- Leaves
- 252
- Series
- International Series of Numerical Mathematics/Internationale Schriftenreihe zur Numerischen Mathematik/Série internationale d’Analyse numérique 89
- Edition
- 1
- Category
- Library
⬇ Acquire This Volume
No coin nor oath required. For personal study only.
✦ Synopsis
- 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.
✦ Table of Contents
Front Matter....Pages 1-9
Quaternionic Analysis....Pages 11-47
Operators....Pages 48-63
Orthogonal Decomposition of the Space L 2,H (G)....Pages 64-66
Some Boundary Value Problems of Dirichlet’s Type....Pages 67-121
H-Regular Boundary Collocation Methods....Pages 122-152
Discrete Quaternionic Function Theory....Pages 153-209
Back Matter....Pages 210-253
✦ Subjects
Science, general
📜 SIMILAR VOLUMES
Methods for Analysis of Nonlinear Ellipt
✍ I. V. Skrypnik
📂 Library
📅 1994
🏛 American Mathematical Society
🌐 English
The theory of nonlinear elliptic equations is currently one of the most actively developing branches of the theory of partial differential equations. This book investigates boundary value problems for nonlinear elliptic equations of arbitrary order. In addition to monotone operator methods, a broad
Harmonic Analysis Techniques for Second
✍ Carlos E. Kenig
📂 Library
📅 1994
🏛 American Mathematical Society
🌐 English
In recent years, there has been a great deal of activity in the study of boundary value problems with minimal smoothness assumptions on the coefficients or on the boundary of the domain in question. These problems are of interest both because of their theoretical importance and the implications for
Harmonic Analysis Techniques for Second
✍ Carlos E. Kenig
📂 Library
📅 1994
🏛 American Mathematical Society
🌐 English
In recent years, there has been a great deal of activity in the study of boundary value problems with minimal smoothness assumptions on the coefficients or on the boundary of the domain in question. These problems are of interest both because of their theoretical importance and the implications for
Wavelet Methods — Elliptic Boundary Valu
✍ Prof. Dr. rer. nat. Angela Kunoth (auth.)
📂 Library
📅 2001
🏛 Vieweg+Teubner Verlag
🌐 English
<p>This research monograph deals with applying recently developed wavelet methods to stationary operator equations involving elliptic differential equations. Particular emphasis is placed on the treatment of the boundary and the boundary conditions.<br> While wavelets have since their discovery main
Boundary value problems for elliptic sys
✍ J. T. Wloka, B. Rowley, B. Lawruk
📂 Library
📅 1995
🏛 Cambridge University Press
🌐 English
The theory of boundary value problems for elliptic systems of partial differential equations has many applications in mathematics and the physical sciences. The aim of this book is to "algebraize" the index theory by means of pseudo-differential operators and new methods in the spectral theory of ma