Strongly elliptic systems and boundary integral equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapore ; Sao Paulo ; Delhi ; Dubai ; Tokyo ; Mexico City
Cambridge University Press
2000
|
| Edition: | First published |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xiv, 357 Seiten |
| ISBN: | 0521663326 9780521663328 052166375X 9780521663755 |
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MARC
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| 100 | 1 | |a McLean, William |d 1960- |0 (DE-588)173409075 |4 aut | |
| 245 | 1 | 0 | |a Strongly elliptic systems and boundary integral equations |c William McLean |
| 250 | |a First published | ||
| 264 | 1 | |a Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapore ; Sao Paulo ; Delhi ; Dubai ; Tokyo ; Mexico City |b Cambridge University Press |c 2000 | |
| 300 | |a xiv, 357 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Boundary element methods | |
| 650 | 4 | |a Differential equations, Elliptic | |
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| 650 | 0 | 7 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text |
Contents
Preface
page
xi
1.
Introduction
1
Exercises
15
2.
Abstract Linear Equations
17
The Kernel and Image
18
Duality
20
Compactness
27
Fredholm
Operators
32
Hubert Spaces
38
Coercivity
42
Elementary Spectral Theory
45
Exercises
52
3.
Sobolev Spaces
57
Convolution
58
Differentiation
61
Schwartz Distributions
64
Fourier Transforms
69
Sobolev Spaces
-
First Definition
73
Sobolev Spaces
-
Second Definition
75
Equivalence of the Norms
79
Localisation and Changes of Coordinates
83
Density and Imbedding Theorems
85
Lipschitz Domains
89
Sobolev Spaces on the Boundary
96
The Trace Operator
100
Vector-Valued Functions
106
Exercises
107
vii
viii Contents
4.
Strongly Elliptic
Systems
113
The First and Second Green Identities
113
Strongly Elliptic Operators
118
Boundary Value Problems
128
Regularity of Solutions
1
3 З
The Transmission Property
141
Estimates for the
Steklov-Poincaré
Operator
145
Exercises
156
5.
Homogeneous Distributions
158
Finite-Part Integrals
159
Extension from R" \
{0}
to R"
166
Fourier Transforms
169
Change of Variables
174
Finite-Part Integrals on Surfaces
181
Exercises
187
6.
Surface Potentials
191
Parametrices
192
Fundamental Solutions
197
The Third Green Identity
200
Jump Relations and Mapping Properties
202
Duality Relations
211
Exercises
215
7.
Boundary Integral Equations
217
Operators on the Boundary
217
Integral Representations
219
The Dirichlet Problem
226
The Neumann Problem
229
Mixed Boundary Conditions
231
Exterior Problems
234
Regularity Theory
239
Exercises
241
8.
The Laplace Equation
246
Fundamental Solutions
247
Spherical Harmonics
250
Behaviour at Infinity
258
Solvability for the Dirichlet Problem
260
Solvability for the Neumann Problem
266
Exercises
268
Contents ix
9.
The Helmholtz Equation
276
Separation
of
Variables 277
The Sommerfeld Radiation
Condition
280
Uniqueness and Existence of Solutions
286
A Boundary Integral Identity
289
Exercises
293
10.
Linear Elasticity
296
Korn's Inequality
297
Fundamental Solutions
299
Uniqueness Results
301
Exercises
305
Appendix A. Extension Operators for Sobolev Spaces
309
Exercises
315
Appendix B. Interpolation Spaces
317
The ^-Method
318
TheJ-Method
321
Interpolation of Sobolev Spaces
329
Exercises
333
Appendix C. Further Properties of Spherical Harmonics
334
Exercises
338
References
341
Index
347
Index of Notation
353
Partial
differential equations provide mathematical models
of many important problems in the physical sciences and
engineering. This book treats one class of such equations,
concentrating on methods involving the use of surface
potentials. It provides the first detailed exposition of the
mathematical theory of boundary integral equations of the first
kind on non-smooth domains. Included are chapters on three
specific examples: the Laplace equation, the Helmholtz equa¬
tion and the equations of linear elasticity.
The book is designed to provide an ideal preparation for
studying the modern research literature on boundary element
methods.
Dr
McLean received his PhD from the Australian National
University, and is currently a Senior Lecturer in Applied
Mathematics at the University of New South Wales. |
| any_adam_object | 1 |
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | First published |
| format | Book |
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| id | DE-604.BV013246287 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-30T09:01:04Z |
| institution | BVB |
| isbn | 0521663326 9780521663328 052166375X 9780521663755 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009028341 |
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| physical | xiv, 357 Seiten |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | McLean, William 1960- (DE-588)173409075 aut Strongly elliptic systems and boundary integral equations William McLean First published Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapore ; Sao Paulo ; Delhi ; Dubai ; Tokyo ; Mexico City Cambridge University Press 2000 xiv, 357 Seiten txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Boundary element methods Differential equations, Elliptic Randelemente-Methode (DE-588)4076508-8 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s Randelemente-Methode (DE-588)4076508-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009028341&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009028341&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | McLean, William 1960- Strongly elliptic systems and boundary integral equations Boundary element methods Differential equations, Elliptic Randelemente-Methode (DE-588)4076508-8 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| subject_GND | (DE-588)4076508-8 (DE-588)4014485-9 |
| title | Strongly elliptic systems and boundary integral equations |
| title_auth | Strongly elliptic systems and boundary integral equations |
| title_exact_search | Strongly elliptic systems and boundary integral equations |
| title_full | Strongly elliptic systems and boundary integral equations William McLean |
| title_fullStr | Strongly elliptic systems and boundary integral equations William McLean |
| title_full_unstemmed | Strongly elliptic systems and boundary integral equations William McLean |
| title_short | Strongly elliptic systems and boundary integral equations |
| title_sort | strongly elliptic systems and boundary integral equations |
| topic | Boundary element methods Differential equations, Elliptic Randelemente-Methode (DE-588)4076508-8 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | Boundary element methods Differential equations, Elliptic Randelemente-Methode Elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009028341&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009028341&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mcleanwilliam stronglyellipticsystemsandboundaryintegralequations |