Ginzburg Landau vortices:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1994
|
| Schriftenreihe: | Progress in nonlinear differential equations and their applications
13 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 154 - 158 |
| Beschreibung: | XXVII, 158 S. |
| ISBN: | 3764337230 0817637230 |
Internformat
MARC
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| 100 | 1 | |a Bethuel, Fabrice |d 1963- |e Verfasser |0 (DE-588)172705657 |4 aut | |
| 245 | 1 | 0 | |a Ginzburg Landau vortices |c Fabrice Bethuel ; Haïm Brezis ; Frédéric Hélein |
| 246 | 1 | 3 | |a Ginzburg-Landau vortices |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1994 | |
| 300 | |a XXVII, 158 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in nonlinear differential equations and their applications |v 13 | |
| 500 | |a Literaturverz. S. 154 - 158 | ||
| 650 | 7 | |a Análise matemática |2 larpcal | |
| 650 | 7 | |a Equations différentielles non linéaires - Solutions numériques |2 ram | |
| 650 | 7 | |a Equações diferenciais parciais hiperbólicas não lineares |2 larpcal | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 7 | |a Singularités (Mathématiques) |2 ram | |
| 650 | 7 | |a Superfluidité - Mathématiques |2 ram | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Differential equations, Nonlinear |x Numerical solutions | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Singularities (Mathematics) | |
| 650 | 4 | |a Superconductors |x Mathematics | |
| 650 | 4 | |a Superfluidity |x Mathematics | |
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| 700 | 1 | |a Hélein, Frédéric |d 1963- |e Verfasser |0 (DE-588)172705681 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1805084264840036352 |
|---|---|
| adam_text |
TABLE OF CONTENTS
Introduction be
I. Energy estimates for S1 valued maps
1. An auxiliary linear problem 1
2. Variants of Theorem I.I 6
3. 51 valued harmonic maps with prescribed isolated
singularities. The canonical harmonic map 10
4. Shrinking holes. Renormalized energy 16
II. A lower bound for the energy of S1 valued maps
on perforated domains 31
III. Some basic estimates for ue
1. Estimates when G = Br and g[x) = x/\x\ 42
2. An upper bound for Ee(ue) 44
3. An upper bound for 4j JG(|u£|2 — I)2 45
4. |u£| 1/2 on "good discs" 46
IV. Towards locating the singularities:
bad discs and good discs
1. A covering argument 48
2. Modifying the bad discs 49
V. An upper bound for the energy of ue away from
the singularities
1. A lower bound for the energy of uE near ctj 53
2. Proof of Theorem V.I 54
CONTENTS
VI. uCn converges: «t is born!
1. Proof of Theorem VI. 1 58
2. Further properties of u+ : singularities have degree
one and they are not on the boundary 60
VII. ut coincides with THE canonical harmonic map
having singularities (oj) 65
VIII. The configuration (a_,) minimizes the renormal
ized energy W
1. The general case 76
2. The vanishing gradient property and its various
forms 82
3. Construction of critical points of the renormalized
energy 93
4. The case G = Bx and g[0) = eie 95
5. The case G = Bx and g(9) = edie with d 2 97
IX. Some additional properties of uc
1. The zeroes of uc 100
2. The limit of {Ec{uc) 7rd\ log e\} as e 0 101
3. /G |V|u£||2 remains bounded as e — 0 103
4. The bad discs revisited 104
X. Non minimizing solutions of the Ginzburg Landau
equation
1. Preliminary estimates; bad discs and good discs 107
2. Splitting \Vvc\ 109
3. Study of the associated linear problems 112
4. The basic estimates: JG \Vvc\2 C\ log e\ and
/G|V^|P CP forp 2 119
5. vCn converges to i»* 125
6. Properties of v+ 132
CONTENTS
XI. Open problems 137
Appendix I. Summary of the basic convergence re¬
sults in the case where deg(g, dG) = 0 142
Appendix II. Radial solutions 145
Appendix III. Quantization effects for the equation
Av = v(l \v\2) in R2 147
Appendix IV. The energy of maps on perforated do¬
mains revisited 148
BIBLIOGRAPHY 154
INDEX 159 |
| any_adam_object | 1 |
| author | Bethuel, Fabrice 1963- Brézis, Haïm 1944-2024 Hélein, Frédéric 1963- |
| author_GND | (DE-588)172705657 (DE-588)135645921 (DE-588)172705681 |
| author_facet | Bethuel, Fabrice 1963- Brézis, Haïm 1944-2024 Hélein, Frédéric 1963- |
| author_role | aut aut aut |
| author_sort | Bethuel, Fabrice 1963- |
| author_variant | f b fb h b hb f h fh |
| building | Verbundindex |
| bvnumber | BV009628954 |
| callnumber-first | Q - Science |
| callnumber-label | QC20 |
| callnumber-raw | QC20.7.S54 |
| callnumber-search | QC20.7.S54 |
| callnumber-sort | QC 220.7 S54 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 540 SK 950 |
| classification_tum | PHY 011f MAT 354f |
| ctrlnum | (OCoLC)29754519 (DE-599)BVBBV009628954 |
| dewey-full | 530.1/55353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/55353 |
| dewey-search | 530.1/55353 |
| dewey-sort | 3530.1 555353 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| genre | 1\p (DE-588)1071861417 Konferenzschrift 2002 Shanghai gnd-content |
| genre_facet | Konferenzschrift 2002 Shanghai |
| id | DE-604.BV009628954 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T08:01:42Z |
| institution | BVB |
| isbn | 3764337230 0817637230 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006363731 |
| oclc_num | 29754519 |
| open_access_boolean | |
| owner | DE-12 DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-83 DE-11 DE-188 |
| physical | XXVII, 158 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spelling | Bethuel, Fabrice 1963- Verfasser (DE-588)172705657 aut Ginzburg Landau vortices Fabrice Bethuel ; Haïm Brezis ; Frédéric Hélein Ginzburg-Landau vortices Boston [u.a.] Birkhäuser 1994 XXVII, 158 S. txt rdacontent n rdamedia nc rdacarrier Progress in nonlinear differential equations and their applications 13 Literaturverz. S. 154 - 158 Análise matemática larpcal Equations différentielles non linéaires - Solutions numériques ram Equações diferenciais parciais hiperbólicas não lineares larpcal Physique mathématique ram Singularités (Mathématiques) ram Superfluidité - Mathématiques ram Mathematik Mathematische Physik Differential equations, Nonlinear Numerical solutions Mathematical physics Singularities (Mathematics) Superconductors Mathematics Superfluidity Mathematics Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Ginzburg-Landau-Gleichung (DE-588)4157356-0 gnd rswk-swf Supraleitung (DE-588)4058651-0 gnd rswk-swf Suprafluidität (DE-588)4184132-3 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 2002 Shanghai gnd-content Ginzburg-Landau-Gleichung (DE-588)4157356-0 s Mathematische Physik (DE-588)4037952-8 s 2\p DE-604 Supraleitung (DE-588)4058651-0 s 3\p DE-604 Nichtlineare Differentialgleichung (DE-588)4205536-2 s 4\p DE-604 Suprafluidität (DE-588)4184132-3 s 5\p DE-604 Brézis, Haïm 1944-2024 Verfasser (DE-588)135645921 aut Hélein, Frédéric 1963- Verfasser (DE-588)172705681 aut Progress in nonlinear differential equations and their applications 13 (DE-604)BV007934389 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006363731&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bethuel, Fabrice 1963- Brézis, Haïm 1944-2024 Hélein, Frédéric 1963- Ginzburg Landau vortices Progress in nonlinear differential equations and their applications Análise matemática larpcal Equations différentielles non linéaires - Solutions numériques ram Equações diferenciais parciais hiperbólicas não lineares larpcal Physique mathématique ram Singularités (Mathématiques) ram Superfluidité - Mathématiques ram Mathematik Mathematische Physik Differential equations, Nonlinear Numerical solutions Mathematical physics Singularities (Mathematics) Superconductors Mathematics Superfluidity Mathematics Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Ginzburg-Landau-Gleichung (DE-588)4157356-0 gnd Supraleitung (DE-588)4058651-0 gnd Suprafluidität (DE-588)4184132-3 gnd |
| subject_GND | (DE-588)4205536-2 (DE-588)4037952-8 (DE-588)4157356-0 (DE-588)4058651-0 (DE-588)4184132-3 (DE-588)1071861417 |
| title | Ginzburg Landau vortices |
| title_alt | Ginzburg-Landau vortices |
| title_auth | Ginzburg Landau vortices |
| title_exact_search | Ginzburg Landau vortices |
| title_full | Ginzburg Landau vortices Fabrice Bethuel ; Haïm Brezis ; Frédéric Hélein |
| title_fullStr | Ginzburg Landau vortices Fabrice Bethuel ; Haïm Brezis ; Frédéric Hélein |
| title_full_unstemmed | Ginzburg Landau vortices Fabrice Bethuel ; Haïm Brezis ; Frédéric Hélein |
| title_short | Ginzburg Landau vortices |
| title_sort | ginzburg landau vortices |
| topic | Análise matemática larpcal Equations différentielles non linéaires - Solutions numériques ram Equações diferenciais parciais hiperbólicas não lineares larpcal Physique mathématique ram Singularités (Mathématiques) ram Superfluidité - Mathématiques ram Mathematik Mathematische Physik Differential equations, Nonlinear Numerical solutions Mathematical physics Singularities (Mathematics) Superconductors Mathematics Superfluidity Mathematics Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Ginzburg-Landau-Gleichung (DE-588)4157356-0 gnd Supraleitung (DE-588)4058651-0 gnd Suprafluidität (DE-588)4184132-3 gnd |
| topic_facet | Análise matemática Equations différentielles non linéaires - Solutions numériques Equações diferenciais parciais hiperbólicas não lineares Physique mathématique Singularités (Mathématiques) Superfluidité - Mathématiques Mathematik Mathematische Physik Differential equations, Nonlinear Numerical solutions Mathematical physics Singularities (Mathematics) Superconductors Mathematics Superfluidity Mathematics Nichtlineare Differentialgleichung Ginzburg-Landau-Gleichung Supraleitung Suprafluidität Konferenzschrift 2002 Shanghai |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006363731&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007934389 |
| work_keys_str_mv | AT bethuelfabrice ginzburglandauvortices AT brezishaim ginzburglandauvortices AT heleinfrederic ginzburglandauvortices |