Constructive methods for linear and nonlinear boundary value problems for analytic functions: theory and applications
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall, CRC
2000
|
| Schriftenreihe: | Chapman & Hall/CRC monographs and surveys in pure and applied mathematics
108 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009203538&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | VIII, 283 S. |
| ISBN: | 1584880570 |
Internformat
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Datensatz im Suchindex
| _version_ | 1819286943628787712 |
|---|---|
| adam_text | Titel: Constructive methods for linear and nonlinear boundary value problems for analytic functions
Autor: Mityushev, Vladimir V
Jahr: 2000
Contents
Preface v
1 Historical Survey 1
2 Notations and Auxiliary Results 9
2.1 Geometry of complex plane..................................................9
2.2 Functional spaces...............................12
2.3 Operator equations in functional spaces..................18
2.4 Properties of analytic and harmonic functions...............22
2.5 Boundary properties.............................23
2.6 Cauchy type integral and singular integrals................26
2.7 Schwarz operator...............................30
2.7.1 Schwarz operator and complex Green function for simply con-
nected domain............................30
2.7.2 Complex Green function and Schwarz operator for
multiply connected domain.....................32
2.8 C-linear conjugation problem........................37
2.8.1 Simply connected domain......................37
2.8.2 Multiply connected domain.....................40
2.8.3 Glinear conjugation problem on open arcs.............41
2.9 Riemann-Hilbert boundary value problem.................42
2.10 Entire functions...............................45
2.11 Conformal mappings.............................50
2.12 R-linear problem and its applications...................52
2.13 Notes and Comments............................55
3 Nonlinear boundary value problems 57
3.1 Conjugation problem of power type.....................57
CONTENTS
3.1.1 Homogeneous problem.......................58
3.1.2 Solution to nonlinear conjugation problem of power type with
admissible zeros on the contour...................54
3.1.3 Inhomogeneous problem.......................70
3.2 Problem of multiplication type.......................73
3.3 Entire functions methods..........................75
3.3.1 Multiplication type problem for an open arc............75
3.3.2 Multiplication type problem for a compound contour.......85
3.4 General Riemann-Hilbert problem of power type.............100
3.4.1 Homogeneous problem with positive integer exponent.......101
3.4.2 Homogeneous problem with real exponent. ............104
3.4.3 Homogeneous problem with complex exponent..........106
3.5 The modulus problem and its generalization................108
3.5.1 Simple problem on modulus.....................108
3.5.2 Generalized problem on modulus of an analytic
function................................Ill
3.6 Linear fractional problem..........................113
3.7 Cherepanov s mixed problem........................118
3.7.1 Statement of the problem. Simple cases of solvability.......118
3.7.2 Meromorphic solutions........................119
3.7.3 Analytic solutions for n 2.....................124
3.8 Notes and Comments............................127
4 Method of Functional Equations 129
4.1 Dirichlet problem for a doubly connected domain.............129
4.2 A nonlinear boundary value problem....................134
4.2.1 General approach...........................134
4.2.2 A problem for a doubly connected domain.............137
4.2.3 A nonlinear boundary value problem and functional equation. . 138
4.3 Linear functional equations.........................145
4.4 Harmonic measures and Schwarz operator.................149
4.4.1 Harmonic measures.........................149
4.4.2 Schwarz operator...........................154
4.5 Linear Riemann-Hilbert problem......................159
4.6 Poincare series................................................164
4.7 Mixed problem for multiply connected domains..............170
4.8 Circular polygons with zero angles...................173
CONTENTS
4.9 Generalized method of Schwarz and other
methods....................................181
4.9.1 Generalized method of Schwarz for a doubly connected domain. 181
4.9.2 Generalized method of Schwarz for multiply connected domains
and other methods..........................184
4.9.3 The modified method of Schwarz..................189
4.10 Notes and Comments............................194
5 Nonlinear Problems of Mechanics 199
5.1 Steady heat conduction. Nonlinear composites..............199
5.2 Linearized problem..............................206
5.2.1 Linearized problem for circular domains..............207
5.2.2 A mixed problem for a circular domain...............209
5.2.3 A mixed boundary value problem..................213
5.3 Constructive solution to integral equations.................219
5.4 Composite materials with reactive inclusions................222
5.5 Steady heat conduction on configurations.................225
5.5.1 A special surface...........................226
5.5.2 Configurations............................228
5.6 An elastic problem for composite materials................235
5.7 Plane Stokes flow...............................242
5.8 Notes and Comments............................255
Bibliography 257
Index 281
|
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| id | DE-604.BV013484302 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:48:08Z |
| institution | BVB |
| isbn | 1584880570 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009203538 |
| oclc_num | 42290588 |
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| owner | DE-29T DE-703 DE-634 DE-188 |
| owner_facet | DE-29T DE-703 DE-634 DE-188 |
| physical | VIII, 283 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Chapman & Hall, CRC |
| record_format | marc |
| series | Chapman & Hall/CRC monographs and surveys in pure and applied mathematics |
| series2 | Chapman & Hall/CRC monographs and surveys in pure and applied mathematics |
| spellingShingle | Mitiuszew, Władimir 1958- Rogosin, Sergei V. 1952- Constructive methods for linear and nonlinear boundary value problems for analytic functions theory and applications Chapman & Hall/CRC monographs and surveys in pure and applied mathematics Problèmes aux limites - Fonctions analytiques ram Analytic functions Boundary value problems Konstruktive Methode (DE-588)4165106-6 gnd Randwertproblem (DE-588)4048395-2 gnd Analytische Funktion (DE-588)4142348-3 gnd |
| subject_GND | (DE-588)4165106-6 (DE-588)4048395-2 (DE-588)4142348-3 |
| title | Constructive methods for linear and nonlinear boundary value problems for analytic functions theory and applications |
| title_auth | Constructive methods for linear and nonlinear boundary value problems for analytic functions theory and applications |
| title_exact_search | Constructive methods for linear and nonlinear boundary value problems for analytic functions theory and applications |
| title_full | Constructive methods for linear and nonlinear boundary value problems for analytic functions theory and applications Vladimir V. Mityushev ; Sergei V. Rogosin |
| title_fullStr | Constructive methods for linear and nonlinear boundary value problems for analytic functions theory and applications Vladimir V. Mityushev ; Sergei V. Rogosin |
| title_full_unstemmed | Constructive methods for linear and nonlinear boundary value problems for analytic functions theory and applications Vladimir V. Mityushev ; Sergei V. Rogosin |
| title_short | Constructive methods for linear and nonlinear boundary value problems for analytic functions |
| title_sort | constructive methods for linear and nonlinear boundary value problems for analytic functions theory and applications |
| title_sub | theory and applications |
| topic | Problèmes aux limites - Fonctions analytiques ram Analytic functions Boundary value problems Konstruktive Methode (DE-588)4165106-6 gnd Randwertproblem (DE-588)4048395-2 gnd Analytische Funktion (DE-588)4142348-3 gnd |
| topic_facet | Problèmes aux limites - Fonctions analytiques Analytic functions Boundary value problems Konstruktive Methode Randwertproblem Analytische Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009203538&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013350872 |
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