Introduction to heat potential theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2012
|
| Series: | Mathematical surveys and monographs
182 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 259-262) and index |
| Physical Description: | XIII, 266 S. 26 cm |
| ISBN: | 9780821849989 0821849980 |
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MARC
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| 245 | 1 | 0 | |a Introduction to heat potential theory |c Neil A. Watson |
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Record in the Search Index
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| adam_text | Titel: Introduction to heat potential theory
Autor: Watson, Neil
Jahr: 2012
Contents
Preface vii
Notation and Terminology xi
Chapter 1. The Heat Operator, Temperatures and Mean Values 1
1.1. Temperatures and Heat Balls 1
1.2. Mean Values of Smooth Functions over Heat Spheres 3
1.3. Mean Values of Smooth Subtemperatures over Heat Spheres 7
1.4. Mean Values of Smooth Subtemperatures over Heat Balls 13
1.5. The Boundary Maximum Principle on Circular Cylinders 17
1.6. Modified Heat Balls 19
1.7. Harnack Theorems 25
1.8. Equicontinuous Families of Temperatures 29
1.9. Notes and Comments 31
Chapter 2. The Poisson Integral for a Circular Cylinder 35
2.1. The Cauchy Problem on a Half-Space 35
2.2. The Dirichlet Problem on a Circular Cylinder 37
2.3. Double Layer Heat Potentials 39
2.4. The Poisson Integral and the Caloric Measure 44
2.5. Characterizations of Temperatures 47
2.6. Extensions of some Harnack Theorems 51
2.7. Notes and Comments 52
Chapter 3. Subtemperatures and the Dirichlet Problem on Convex Domains
of Revolution 53
3.1. Semicontinuous Functions 53
3.2. Subtemperatures 55
3.3. The Dirichlet Problem on Convex Domains of Revolution 64
3.4. Boundary Behaviour of the PWB Solution 69
3.5. Characterizations of Hypotemperatures and Subtemperatures 71
3.6. Properties of Hypotemperatures 80
3.7. Thermic Majorants 82
3.8. Notes and Comments 83
Chapter 4. Temperatures on an Infinite Strip 85
4.1. An Extension of the Maximum Principle on an Infinite Strip 85
4.2. Gauss-Weierstrass Integrals 87
4.3. Nonnegative Temperatures 95
4.4. Minimality of the Fundamental Temperature 101
4.5. Notes and Comments 103
Chapter 5. Classes of Subtemperatures on an Infinite Strip 105
5.1. Hyperplane Mean Values and Classes of Subtemperatures 105
5.2. Behaviour of the Hyperplane Mean Values of Subtemperatures 114
5.3. Classes of Subtemperatures and Nonnegative Thermic Majorants 119
5.4. Characterizations of the Gauss-Weierstrass Integrals of Functions 123
5.5. Notes and Comments 126
Chapter 6. Green Functions and Heat Potentials 127
6.1. Green Functions 127
6.2. Green Functions and the Adjoint Heat Equation 131
6.3. Heat Potentials 134
6.4. The Distributional Heat Operator 140
6.5. The Riesz Decomposition Theorem 146
6.6. Monotone Approximation by Smooth Supertemperatures 150
6.7. Further Characterizations of Subtemperatures 151
6.8. Supertemperatures on an Infinite Strip or Half-Space 152
6.9. Notes and Comments 157
Chapter 7. Polar Sets and Thermal Capacity 159
7.1. Polar Sets 159
7.2. Families of Supertemperatures 162
7.3. The Natural Order Decomposition 166
7.4. Reductions and Smoothed Reductions 170
7.5. The Thermal Capacity of Compact Sets 175
7.6. The Thermal Capacity of More General Sets 178
7.7. Thermal and Cothermal Capacities 183
7.8. Capacitable Sets 183
7.9. Polar Sets and Heat Potentials 187
7.10. Thermal Capacity and Lebesgue Measure 188
7.11. Notes and Comments 192
Chapter 8. The Dirichlet Problem on Arbitrary Open Sets 195
8.1. Classification of Boundary Points 196
8.2. Upper and Lower PWB Solutions 199
8.3. Resolutivity and PWB Solutions 205
8.4. The Caloric Measure on the Essential Boundary 207
8.5. Boundary Behaviour of PWB Solutions 214
8.6. Geometric Tests for Regularity 222
8.7. Green Functions, Heat Potentials, and Thermal Capacity 225
8.8. Notes and Comments 228
Chapter 9. The Thermal Fine Topology 231
9.1. Definitions and Basic Properties 231
9.2. Further Properties of Reductions 237
9.3. The Fundamental Convergence Theorem 240
9.4. Applications of the Fundamental Convergence Theorem to
Reductions 244
9.5. Thermal Thinness and the Regularity of Normal Boundary Points 249
9.6. Thermal Fine Limits and Euclidean Limits 252
9.7. Thermal Thinness and the Quasi-Lindelof Property 253
9.8. Notes and Comments 257
Bibliography 259
Index 263
|
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| discipline | Mathematik |
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| id | DE-604.BV040553151 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:26:21Z |
| institution | BVB |
| isbn | 9780821849989 0821849980 |
| language | English |
| lccn | 2012004904 |
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| physical | XIII, 266 S. 26 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Watson, N. A. 1948- Verfasser (DE-588)1025827929 aut Introduction to heat potential theory Neil A. Watson Providence, R.I. American Mathematical Society 2012 XIII, 266 S. 26 cm txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 182 Includes bibliographical references (p. 259-262) and index Potential theory (Mathematics) Erscheint auch als Online-Ausgabe 978-0-8218-8792-9 Mathematical surveys and monographs 182 (DE-604)BV000018014 182 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025398897&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Watson, N. A. 1948- Introduction to heat potential theory Mathematical surveys and monographs Potential theory (Mathematics) |
| title | Introduction to heat potential theory |
| title_auth | Introduction to heat potential theory |
| title_exact_search | Introduction to heat potential theory |
| title_full | Introduction to heat potential theory Neil A. Watson |
| title_fullStr | Introduction to heat potential theory Neil A. Watson |
| title_full_unstemmed | Introduction to heat potential theory Neil A. Watson |
| title_short | Introduction to heat potential theory |
| title_sort | introduction to heat potential theory |
| topic | Potential theory (Mathematics) |
| topic_facet | Potential theory (Mathematics) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025398897&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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