Functional analysis in mechanics:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York ; Heidelberg [u.a.]
Springer
2013
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025700602&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Includes bibliographical references and index |
| Umfang: | IX, 308 S. |
| ISBN: | 9781461458678 1461458676 |
Internformat
MARC
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| 100 | 1 | |a Lebedev, Leonid P. |d 1946- |e Verfasser |0 (DE-588)124355560 |4 aut | |
| 245 | 1 | 0 | |a Functional analysis in mechanics |c L. P. Lebedev ; I. I. Vorovich ; Michael J. Cloud |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York ; Heidelberg [u.a.] |b Springer |c 2013 | |
| 300 | |a IX, 308 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Functional analysis | |
| 650 | 0 | 7 | |a Angewandte Mathematik |0 (DE-588)4142443-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kontinuumsmechanik |0 (DE-588)4032296-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Operatortheorie |0 (DE-588)4075665-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Kontinuumsmechanik |0 (DE-588)4032296-8 |D s |
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| 689 | 1 | 3 | |a Operatortheorie |0 (DE-588)4075665-8 |D s |
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| 700 | 1 | |a Vorovič, Iosif I. |d 1920-2001 |e Verfasser |0 (DE-588)120780178 |4 aut | |
| 700 | 1 | |a Cloud, Michael J. |d 1960- |e Verfasser |0 (DE-588)120264242 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025700602&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-025700602 | |
Datensatz im Suchindex
| _version_ | 1819295514873561088 |
|---|---|
| adam_text | Contents
Introduction
Metric,
Banach, and Hubert Spaces.............................. 9
. 1
Preliminaries
.............................................. 9
.2
Holder s Inequality and Minkowski s Inequality
................. 14
.3
Metric Spaces of Functions
..................................
IX
.4
Some Relations for the Metrics in
ϋ (Ω)
and f
................. 22
.5
Metrics in Energy Spaces
.................................... 24
.6
Sets in a Metric Space
....................................... 28
.7
Convergence in a Metric Space
............................... 29
.8
Completeness
.............................................. 30
.9
Completion Theorem
....................................... 31
.10
Lebesgue Integrals and the Space W(Q)
........................ 34
.11
Banach Spaces
............................................. 39
.12
Norms on
n-Dimensional
Spaces
.............................. 42
.13
Other Examples of Banach Spaces
............................ 44
.14
Hubert Spaces
............................................. 48
.15
Factor Spaces
.............................................. 50
.16
Separability
............................................... 53
. 17
Compactness, Hausdorff Criterion
............................. 58
. 18
Arzelà s
Theorem and Its Applications
......................... 61
.19
Theory of Approximation in a Normed Space
................... 66
.20
Decomposition Theorem, Riesz Representation
................. 70
.21
Linear Operators and Functionals
............................. 72
.22
Space of Linear Continuous Operators
......................... 76
.23
Uniform Boundedness Theorem
.............................. 79
.24
Banach-Steinhaus Principle
.................................. 82
.25
Closed Operators and the Closed Graph Theorem
................ 83
.26
Inverse Operator
........................................... 89
.27
Lax-Milgram Theorem
...................................... 92
.28
Open Mapping Theorem
..................................... 93
Contents
1.29 Dual Spaces............................................... 94
1.30 Hahn-Banach Theorem..................................... 98
1.31
Consequences of the
Hahn-Banach Theorem...................102
1.32
Contraction Mapping Principle
...............................103
1.33
Topology, Weak and Weak* Topologies
........................109
1.34
Weak Topology in a Normed Space X
.........................
Ill
1.35
Conclusion and Further Reading
..............................113
Mechanics Problems from the Functional Analysis Viewpoint
.......115
2.1
Introduction to Sobolev Spaces
...............................115
2.2
Operator of Imbedding
......................................119
2.3
Some Energy Spaces
........................................120
2.4
Generalized Solutions in Mechanics
...........................135
2.5
Existence of Energy Solutions to Some Mechanics Problems
......141
2.6
Operator Formulation of an Eigenvalue Problem
.................142
2.7
Problem of Elastico-Plasticity; Small Deformations
..............144
2.8
Bases and Complete Systems; Fourier Series
....................151
2.9
Weak Convergence in a Hubert Space
.........................157
2.10 Ritz
and
Bubnov -Gal
erkin Methods
...........................166
2.11
Curvilinear Coordinates, Nonhomogeneous
Boundary Conditions
.......................................168
2.12
Bramble-Hilbert Lemma and Its Applications
...................171
Some Spectral Problems of Mechanics
............................177
3.1
Introduction
...............................................177
3.2
Adjoint Operator
...........................................178
3.3
Compact Operators
.........................................185
3.4
Compact Operators in Hubert Space
...........................190
3.5
Functions Taking Values in a Banach Space
....................192
3.6
Spectrum of a Linear Operator
................................195
3.7
Resolvent Set of a Closed Linear Operator
......................199
3.8
Spectrum of a Compact Operator in Hubert Space
...............201
3.9
Analytic Nature of the Resolvent of a Compact Linear Operator
. . . 209
3.10
Spectrum of a Holomorphic Compact Operator Function
..........211
3.11
Self-Adjoint Compact Linear Operator in Hubert Space
..........213
3.12
Some Applications of Spectral Theory
.........................219
3.13
Courant s Minimax Pnnciple
.................................222
Elements of Nonlinear Functional Analysis
........................225
4.1
Fréchet
and
Gâteaux
Derivatives
..............................225
4.2
Liapunov-Schmidt Method
..................................231
4.3
Critical Points of a Functional
................................233
4.4
Von Kármán
Equations of a Plate
.............................236
4.5
Buckling of a Thin Elastic Shell
..............................243
4.6
Nonlinear Equilibrium Problem for an Elastic Shallow Shell
......251
Contents
їх
4.7
Degree Theory
.............................................255
4.8
Steady-State Flow of a Viscous Liquid
.........................258
Summary of Inequalities and Imbeddings
.............................265
A.I Inequalities
................................................265
A.2 Imbeddings
................................................268
Hints for Selected Problems
.........................................269
References
.........................................................299
In
Memoriam:
Iosif I. Vorovich
......................................301
Index
.............................................................303
|
| any_adam_object | 1 |
| author | Lebedev, Leonid P. 1946- Vorovič, Iosif I. 1920-2001 Cloud, Michael J. 1960- |
| author_GND | (DE-588)124355560 (DE-588)120780178 (DE-588)120264242 |
| author_facet | Lebedev, Leonid P. 1946- Vorovič, Iosif I. 1920-2001 Cloud, Michael J. 1960- |
| author_role | aut aut aut |
| author_sort | Lebedev, Leonid P. 1946- |
| author_variant | l p l lp lpl i i v ii iiv m j c mj mjc |
| building | Verbundindex |
| bvnumber | BV040720363 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)825163038 (DE-599)BSZ375379479 |
| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV040720363 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T16:24:10Z |
| institution | BVB |
| isbn | 9781461458678 1461458676 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025700602 |
| oclc_num | 825163038 |
| open_access_boolean | |
| owner | DE-11 DE-29T DE-355 DE-BY-UBR DE-862 DE-BY-FWS DE-188 |
| owner_facet | DE-11 DE-29T DE-355 DE-BY-UBR DE-862 DE-BY-FWS DE-188 |
| physical | IX, 308 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spellingShingle | Lebedev, Leonid P. 1946- Vorovič, Iosif I. 1920-2001 Cloud, Michael J. 1960- Functional analysis in mechanics Functional analysis Angewandte Mathematik (DE-588)4142443-8 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd Operatortheorie (DE-588)4075665-8 gnd Metrischer Raum (DE-588)4169745-5 gnd Mechanik (DE-588)4038168-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4142443-8 (DE-588)4032296-8 (DE-588)4075665-8 (DE-588)4169745-5 (DE-588)4038168-7 (DE-588)4018916-8 |
| title | Functional analysis in mechanics |
| title_auth | Functional analysis in mechanics |
| title_exact_search | Functional analysis in mechanics |
| title_full | Functional analysis in mechanics L. P. Lebedev ; I. I. Vorovich ; Michael J. Cloud |
| title_fullStr | Functional analysis in mechanics L. P. Lebedev ; I. I. Vorovich ; Michael J. Cloud |
| title_full_unstemmed | Functional analysis in mechanics L. P. Lebedev ; I. I. Vorovich ; Michael J. Cloud |
| title_short | Functional analysis in mechanics |
| title_sort | functional analysis in mechanics |
| topic | Functional analysis Angewandte Mathematik (DE-588)4142443-8 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd Operatortheorie (DE-588)4075665-8 gnd Metrischer Raum (DE-588)4169745-5 gnd Mechanik (DE-588)4038168-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Angewandte Mathematik Kontinuumsmechanik Operatortheorie Metrischer Raum Mechanik Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025700602&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lebedevleonidp functionalanalysisinmechanics AT voroviciosifi functionalanalysisinmechanics AT cloudmichaelj functionalanalysisinmechanics |