Degree theory in analysis and applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1995
|
| Schriftenreihe: | Oxford lecture series in mathematics and its applications
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 211 S. graph. Darst. |
| ISBN: | 0198511965 |
Internformat
MARC
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| 100 | 1 | |a Fonseca, Irene |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Degree theory in analysis and applications |c Irene Fonseca and Wilfrid Gangbo |
| 264 | 1 | |a Oxford |b Clarendon Press |c 1995 | |
| 300 | |a VIII, 211 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford lecture series in mathematics and its applications |v 2 | |
| 490 | 0 | |a Oxford science publications | |
| 650 | 4 | |a Analyse fonctionnelle | |
| 650 | 7 | |a Analyse fonctionnelle |2 ram | |
| 650 | 4 | |a Degré topologique | |
| 650 | 7 | |a Degré topologique |2 ram | |
| 650 | 4 | |a Sobolev, Espaces de | |
| 650 | 7 | |a Théorie degré |2 Jussieu | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Topological degree | |
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| 700 | 1 | |a Gangbo, Wilfrid |d 1961- |e Verfasser |0 (DE-588)121718042 |4 aut | |
| 830 | 0 | |a Oxford lecture series in mathematics and its applications |v 2 |w (DE-604)BV009910017 |9 2 | |
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Datensatz im Suchindex
| _version_ | 1804124924144517120 |
|---|---|
| adam_text | CONTENTS
Introduction 1
1 Degree theory for continuous functions 5
1.1 Topological degree for C1 functions 5
1.2 Topological degree for continuous functions 16
1.3 Generalization of the degree 20
1.4 Exercises 25
2 Degree theory in finite dimensional spaces 30
2.1 Dependence of the degree on 4 and p 30
2.2 Dependence of the degree on the domain D 32
2.3 The multiplication theorem 35
2.4 An application of Hopf s theorem 39
2.5 Degree and winding number 41
2.6 Exercises 46
3 Some applications of the degree theory to
topology 48
3.1 The Brouwer Fixed Point Theorem 48
3.2 Odd mappings 54
3.3 The Jordan Separation Theorem 64
3.4 Exercises 71
4 Measure theory and Sobolev spaces 74
4.1 Review of measure theory 74
4.2 Hausdorff measures 78
4.3 Overview of Sobolev spaces 87
4.4 p capacity 92
5 Properties of the degree for Sobolev functions 106
5.1 Results of weakly differential mappings 107
5.2 Weakly monotone functions 119
5.3 Change of variables via the multiplicity function 131
5.4 Change of variables via the degree 135
5.5 Change of variables for Sobolev functions 140
6 Local invertibility of Sobolev functions and
applications 149
6.1 Local invertibility in Wl N 149
6.2 Energy functional involving variation of the domain 160
viii CONTENTS
7 Degree in infinite dimensional spaces 172
7.1 Introduction to the Leray Schauder degree 172
7.2 Properties of the Leray Schauder degree 177
7.3 Fixed point theorems 185
7.4 An application of the degree theory to ODEs 190
7.5 First application of the degree theory to PDEs 192
7.6 Second application of the degree theory to PDEs 199
7.7 Exercises 203
References 205
Index 209
|
| any_adam_object | 1 |
| author | Fonseca, Irene Gangbo, Wilfrid 1961- |
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| bvnumber | BV010491545 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 600 |
| classification_tum | MAT 576f |
| ctrlnum | (OCoLC)32739949 (DE-599)BVBBV010491545 |
| dewey-full | 515/.7248 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.7248 |
| dewey-search | 515/.7248 |
| dewey-sort | 3515 47248 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010491545 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:53:23Z |
| institution | BVB |
| isbn | 0198511965 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006990692 |
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| physical | VIII, 211 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Clarendon Press |
| record_format | marc |
| series | Oxford lecture series in mathematics and its applications |
| series2 | Oxford lecture series in mathematics and its applications Oxford science publications |
| spelling | Fonseca, Irene Verfasser aut Degree theory in analysis and applications Irene Fonseca and Wilfrid Gangbo Oxford Clarendon Press 1995 VIII, 211 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford lecture series in mathematics and its applications 2 Oxford science publications Analyse fonctionnelle Analyse fonctionnelle ram Degré topologique Degré topologique ram Sobolev, Espaces de Théorie degré Jussieu Functional analysis Topological degree Abbildungsgrad (DE-588)4140975-9 gnd rswk-swf Abbildungsgrad (DE-588)4140975-9 s DE-604 Gangbo, Wilfrid 1961- Verfasser (DE-588)121718042 aut Oxford lecture series in mathematics and its applications 2 (DE-604)BV009910017 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006990692&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fonseca, Irene Gangbo, Wilfrid 1961- Degree theory in analysis and applications Oxford lecture series in mathematics and its applications Analyse fonctionnelle Analyse fonctionnelle ram Degré topologique Degré topologique ram Sobolev, Espaces de Théorie degré Jussieu Functional analysis Topological degree Abbildungsgrad (DE-588)4140975-9 gnd |
| subject_GND | (DE-588)4140975-9 |
| title | Degree theory in analysis and applications |
| title_auth | Degree theory in analysis and applications |
| title_exact_search | Degree theory in analysis and applications |
| title_full | Degree theory in analysis and applications Irene Fonseca and Wilfrid Gangbo |
| title_fullStr | Degree theory in analysis and applications Irene Fonseca and Wilfrid Gangbo |
| title_full_unstemmed | Degree theory in analysis and applications Irene Fonseca and Wilfrid Gangbo |
| title_short | Degree theory in analysis and applications |
| title_sort | degree theory in analysis and applications |
| topic | Analyse fonctionnelle Analyse fonctionnelle ram Degré topologique Degré topologique ram Sobolev, Espaces de Théorie degré Jussieu Functional analysis Topological degree Abbildungsgrad (DE-588)4140975-9 gnd |
| topic_facet | Analyse fonctionnelle Degré topologique Sobolev, Espaces de Théorie degré Functional analysis Topological degree Abbildungsgrad |
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