Nonlinear boundary value problems for holomorphic functions and singular integral equations /
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| Author / Creator: | Wegert, Elias |
|---|---|
| Imprint: | Berlin : Akademie Verlag, c1992. |
| Description: | 240 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Mathematical research ; v. 65 Mathematical research. Bd. 65. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1402626 |
Table of Contents:
- 1. Auxiliary Material. 1.1. Function Spaces. 1.2. Differentiable Mappings. 1.3. Superposition Operators. 1.4. The Leray-Schauder Degree. 1.5. Holomorphic Functions. 1.6. Boundary Values of Holomorphic Functions. 1.7. Linear Riemann-Hilbert Problems. 1.8. Compact Restriction Manifolds. 1.9. Notes and Comments
- 2. Nonlinear Riemann-Hilbert Problems: Solvability. 2.1. Definitions and Classification. 2.2. Fixed Point Equation. 2.3. A-priori Estimation. 2.4. Fixed Point Index. 2.5. Existence Theorems: Compact Restriction Manifolds. 2.6. Existence Theorems: Noncompact Orientable Restriction Manifolds. 2.7. Existence Theorems: Noncompact Nonorientable Restriction Manifolds. 2.8. Regularity of Solutions. 2.9. Notes and Comments
- 3. Extremal Principles. 3.1. Variability Regions: Compact Manifolds. 3.2. Variability Regions: Noncompact Manifolds. 3.3. Interpolation Problems. 3.4. Deformations of Restriction Manifolds. 3.5. Relations to Classical Topics. 3.6. Notes and Comments
- 4. Parameter-depending Problems. 4.1. Continuity. 4.2. Differentiability. 4.3. Asymptotics of the Indicatrix. 4.4. Variational Formulas
- 5. Singular Integral Equations. 5.1. Singular Integral Equations of Hammerstein Type. 5.2. Implicit Singular Integral Equations. 5.3. Miscellaneous Equations. 5.4. Bifurcation. 5.5. Notes and Comments
- 6. Applications. 6.1. The Problem of Nehari-Helton. 6.2. Minimal H[actual symbol not reproducible]-Interpolation. 6.3. Polynomial Hulls. 6.4. Potential Flow Past a Cylinder with Porous Surface
- 7. Iterative Methods. 7.1. Restriction Manifolds Given in Parametric Form. 7.2. Restriction Manifolds Given by an Equation. 7.3. Problems Depending on Parameters. 7.4. Implementation and Test Results. 7.5. Notes and Comments
- 8. Discrete Riemann-Hilbert Problems. 8.1. Discrete Function Spaces and Interpolation. 8.2. Discrete Linear Riemann-Hilbert Problems. 8.3. Discrete Nonlinear Riemann-Hilbert Problems. 8.4. Discrete Problems Depending on Parameters. 8.5. Implementation and Test Results. 8.6. Notes and Comments.