Classical potential theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Springer
2002
|
| Ausgabe: | 2. print. |
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 317 - 327 |
| Beschreibung: | XVI, 333 S. graph. Darst. |
| ISBN: | 1852336188 |
Internformat
MARC
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| 245 | 1 | 0 | |a Classical potential theory |c David H. Armitage ; Stephen J. Gardiner |
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Datensatz im Suchindex
| _version_ | 1804133418824368128 |
|---|---|
| adam_text | Titel: Classical potential theory
Autor: Armitage, David H
Jahr: 2002
David H. Armitage Stephen J. Gardiner
Classical Potential
Theory
Springer
Contents
Notation and Terminology xiii
1. Harmonic Functions
1.1. Laplace s equation 1
1.2. The mean value property 3
1.3. The Poisson integral for a ball 6
1.4. Harnack s inequalities 13
1.5. Families of harmonic functions: convergence properties . . . . 15
1.6. The Kelvin transform 19
1.7. Harmonic functions on half-spaces 22
1.8. Real-analyticity of harmonic functions 26
1.9. Exercises 30
2. Harmonic Polynomials
2.1. Spaces of homogeneous polynomials 33
2.2. Another inner product on a space of polynomials 35
2.3. Axially symmetric harmonic polynomials 37
2.4. Polynomial expansions of harmonic functions 40
2.5. Laurent expansions of harmonic functions 44
2.6. Harmonic approximation 47
2.7. Harmonic polynomials and classical polynomials 53
2.8. Exercises , 55
3. Subharmonic Functions
3.1. Elementary properties 59
3.2. Criteria for subharmonicity 64
3.3. Approximation of subharmonic functions by smooth ones . . 68
3.4. Convexity and subharmonicity 72
3.5. Mean values and subharmonicity 75
3.6. Harmonic majorants 79
3.7. Families of subharmonic functions: convergence properties . 82
3.8. Exercises 84
x Contents
4. Potentials
4.1. Green functions 89
4.2. Potentials 96
4.3. The distributional Laplacian 100
4.4. The Riesz decomposition 105
4.5. Continuity and smoothness properties 109
4.6. Classical boundary limit theorems 112
4.7. Exercises 118
5. Polar Sets and Capacity
5.1. Polar sets 123
5.2. Removable singularity theorems 127
5.3. Reduced functions 129
5.4. The capacity of a compact set 134
5.5. Inner and outer capacity 137
5.6. Capacitable sets 143
5.7. The fundamental convergence theorem 146
5.8. Logarithmic capacity 150
5.9. Hausdorff measure and capacity 156
5.10. Exercises 159
6. The Dirichlet Problem
6.1. Introduction 163
6.2. Upper and lower PWB solutions 164
6.3. Further properties of PWB solutions 167
6.4. Harmonic measure 172
6.5. Negligible sets . . . ·. 177
6.6. Boundary behaviour 179
6.7. Behaviour near infinity 188
6.8. Regularity and the Green function 189
6.9. PWB solutions and reduced functions 191
6.10. Superharmonic extension 192
6.11. Exercises 193
7. The Fine Topology
7.1. Introduction 197
7.2. Thin sets 199
7.3. Thin sets and reduced functions 201
7.4. Fine limits 206
7.5. Thin sets and the Dirichlet problem 208
7.6. Thinness at infinity 214
7.7. Wiener s criterion 217
7.8. Limit properties of superharmonic functions 221
7.9. Harmonic approximation 226
Contents xi
8. The Martin Boundary
8.1. The Martin kernel and Martin boundary 233
8.2. Reduced functions and minimal harmonic functions 241
8.3. Reductions on Ao and Ai 246
8.4. The Martin representation 250
8.5. The Martin boundary of a strip 252
8.6. The Martin kernel and the Kelvin transform 256
8.7. The boundary Harnack principle for Lipschitz domains . . . . 259
8.8. The Martin boundary of a Lipschitz domain 269
9. Boundary Limits
9.1. Swept measures and the Dirichlet problem for the Martin
compactification 273
9.2. Minimal thinness 279
9.3. Minimal fine limits 284
9.4. The Fatou-Naim-Doob theorem 287
9.5. Minimal thinness in subdomains 290
9.6. Refinements of limit theorems 294
9.7. Minimal thinness in a half-space 296
Appendix 305
Historical Notes 309
References 317
Symbol Index 329
Index 331
|
| any_adam_object | 1 |
| author | Armitage, David H. 1945- Gardiner, Stephen J. 1958- |
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| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9 |
| dewey-search | 515.9 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. print. |
| format | Book |
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| id | DE-604.BV019886358 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:08:24Z |
| institution | BVB |
| isbn | 1852336188 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013210431 |
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| physical | XVI, 333 S. graph. Darst. |
| publishDate | 2002 |
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| publisher | Springer |
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| series2 | Springer monographs in mathematics |
| spelling | Armitage, David H. 1945- Verfasser (DE-588)122123352 aut Classical potential theory David H. Armitage ; Stephen J. Gardiner 2. print. London [u.a.] Springer 2002 XVI, 333 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Literaturverz. S. 317 - 327 Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 s DE-604 Gardiner, Stephen J. 1958- Verfasser (DE-588)122123360 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013210431&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Armitage, David H. 1945- Gardiner, Stephen J. 1958- Classical potential theory Potenzialtheorie (DE-588)4046939-6 gnd |
| subject_GND | (DE-588)4046939-6 |
| title | Classical potential theory |
| title_auth | Classical potential theory |
| title_exact_search | Classical potential theory |
| title_full | Classical potential theory David H. Armitage ; Stephen J. Gardiner |
| title_fullStr | Classical potential theory David H. Armitage ; Stephen J. Gardiner |
| title_full_unstemmed | Classical potential theory David H. Armitage ; Stephen J. Gardiner |
| title_short | Classical potential theory |
| title_sort | classical potential theory |
| topic | Potenzialtheorie (DE-588)4046939-6 gnd |
| topic_facet | Potenzialtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013210431&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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