Degree theory in analysis and applications:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Oxford
Clarendon Press
1995
|
| Schriftenreihe: | Oxford lecture series in mathematics and its applications
2 |
| Schlagwörter: | |
| Links: | 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 |
| Umfang: | VIII, 211 S. graph. Darst. |
| ISBN: | 0198511965 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010491545 | ||
| 003 | DE-604 | ||
| 005 | 19970312 | ||
| 007 | t| | ||
| 008 | 951123s1995 xx d||| |||| 00||| eng d | ||
| 020 | |a 0198511965 |9 0-19-851196-5 | ||
| 035 | |a (OCoLC)32739949 | ||
| 035 | |a (DE-599)BVBBV010491545 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-91G |a DE-29T |a DE-703 |a DE-384 |a DE-824 |a DE-706 |a DE-634 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA612 | |
| 082 | 0 | |a 515/.7248 |2 20 | |
| 084 | |a SK 600 |0 (DE-625)143248: |2 rvk | ||
| 084 | |a MAT 576f |2 stub | ||
| 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 | |
| 650 | 0 | 7 | |a Abbildungsgrad |0 (DE-588)4140975-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Abbildungsgrad |0 (DE-588)4140975-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 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 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006990692 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 576f 2001 A 14514 |
|---|---|
| DE-BY-TUM_katkey | 784387 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020484377 |
| _version_ | 1821938909397909506 |
| 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- |
| author_GND | (DE-588)121718042 |
| author_facet | Fonseca, Irene Gangbo, Wilfrid 1961- |
| author_role | aut aut |
| author_sort | Fonseca, Irene |
| author_variant | i f if w g wg |
| building | Verbundindex |
| bvnumber | BV010491545 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612 |
| callnumber-search | QA612 |
| callnumber-sort | QA 3612 |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01917nam a2200493 cb4500</leader><controlfield tag="001">BV010491545</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19970312 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">951123s1995 xx d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0198511965</subfield><subfield code="9">0-19-851196-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)32739949</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010491545</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA612</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.7248</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 600</subfield><subfield code="0">(DE-625)143248:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 576f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Fonseca, Irene</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Degree theory in analysis and applications</subfield><subfield code="c">Irene Fonseca and Wilfrid Gangbo</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford</subfield><subfield code="b">Clarendon Press</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 211 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Oxford lecture series in mathematics and its applications</subfield><subfield code="v">2</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Oxford science publications</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analyse fonctionnelle</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Analyse fonctionnelle</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Degré topologique</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Degré topologique</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sobolev, Espaces de</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Théorie degré</subfield><subfield code="2">Jussieu</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topological degree</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Abbildungsgrad</subfield><subfield code="0">(DE-588)4140975-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Abbildungsgrad</subfield><subfield code="0">(DE-588)4140975-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gangbo, Wilfrid</subfield><subfield code="d">1961-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)121718042</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Oxford lecture series in mathematics and its applications</subfield><subfield code="v">2</subfield><subfield code="w">(DE-604)BV009910017</subfield><subfield code="9">2</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-006990692</subfield></datafield></record></collection> |
| id | DE-604.BV010491545 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:55:04Z |
| institution | BVB |
| isbn | 0198511965 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006990692 |
| oclc_num | 32739949 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-29T DE-703 DE-384 DE-824 DE-706 DE-634 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-29T DE-703 DE-384 DE-824 DE-706 DE-634 DE-11 DE-188 |
| 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 |
| 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 |
| url | 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 |
| volume_link | (DE-604)BV009910017 |
| work_keys_str_mv | AT fonsecairene degreetheoryinanalysisandapplications AT gangbowilfrid degreetheoryinanalysisandapplications |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 576f 2001 A 14514 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |