Exterior differential systems and Euler-Lagrange partial differential equations:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chicago [u.a.]
Univ. of Chicago Press
2003
|
| Schriftenreihe: | Chicago lectures in mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 213 S. |
| ISBN: | 0226077934 0226077942 |
Internformat
MARC
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| 100 | 1 | |a Bryant, Robert L. |d 1953- |e Verfasser |0 (DE-588)112659721 |4 aut | |
| 245 | 1 | 0 | |a Exterior differential systems and Euler-Lagrange partial differential equations |c Robert Bryant, Phillip Griffiths, and Daniel Grossman |
| 264 | 1 | |a Chicago [u.a.] |b Univ. of Chicago Press |c 2003 | |
| 300 | |a VII, 213 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Chicago lectures in mathematics series | |
| 650 | 7 | |a Análise matemática |2 larpcal | |
| 650 | 4 | |a Lagrange, Équations de | |
| 650 | 7 | |a Pfaffianos |2 larpcal | |
| 650 | 4 | |a Systèmes différentiels extérieurs | |
| 650 | 4 | |a Exterior differential systems | |
| 650 | 4 | |a Lagrange equations | |
| 650 | 0 | 7 | |a Äußeres Differentialsystem |0 (DE-588)4141545-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lagrange-Gleichungen |0 (DE-588)4166461-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lagrange-Gleichungen |0 (DE-588)4166461-9 |D s |
| 689 | 0 | 1 | |a Äußeres Differentialsystem |0 (DE-588)4141545-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Griffiths, Phillip |d 1938- |e Verfasser |0 (DE-588)131881434 |4 aut | |
| 700 | 1 | |a Grossman, Daniel |e Verfasser |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=010258061&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-010258061 | ||
Datensatz im Suchindex
| _version_ | 1804129902846279680 |
|---|---|
| adam_text | Contents
Preface
vii
Introduction
1
1
Lagrangians and Poincaré-Cartan
Forms
9
1.1
Lagrangians
and Contact Geometry
9
1.2
The Euler-Lagrange System
15
1.2.1
Variation of a Legendre Submanifold
15
1.2.2
Calculation of the Euler-Lagrange System
16
1.2.3
The Inverse Problem
18
1.3
Noether s Theorem
22
1.4
Hypersurfaces in Euclidean Space
29
1.4.1
The Contact Manifold over E *1
29
1.4.2
Euclidean-invariant Euler-Lagrange Systems
32
1.4.3
Conservation Laws for Minimal Hypersurfaces
35
2
The Geometry of
Poincaré-Cartan
Forms
45
2.1
The Equivalence Problem for
η
= 2 47
2.2
Neo-Classical
Poincaré-Cartan
Forms
60
2.3
Digression on
Affine
Geometry of Hypersurfaces
66
2.4
The Equivalence Problem for
η
> 3 73
2.5
The Prescribed Mean Curvature System
82
3
Conformally Invariant Euler-Lagrange Systems
87
3.1
Background Material on
Conformai
Geometry
88
3.1.1
Flat
Conformai
Space
88
3.1.2
The
Conformai
Equivalence Problem
93
3.1.3
The
Conformai Laplacian
101
3.2
Conformally Invariant
Poincaré-Cartan
Forms
105
3.3
The
Conformai
Branch of the Equivalence Problem
110
3.4
Conservation Laws for A.u
=
Си^-г
118
3.4.1
The Lie Algebra of Infinitesimal Symmetries
119
3.4.2
Calculation of Conservation Laws
121
Contents
3.5
Conservation
Laws for Wave Equations
126
3.5.1
Energy Density
129
3.5.2
The Conformally Invariant Wave Equation
131
3.5.3
Energy in Three Space Dimensions
135
Additional Topics
141
4.1
The Second Variation
141
4.1.1
A Formula for the Second Variation
141
4.1.2
Relative
Conformai
Geometry
144
4.1.3
Intrinsic Integration by Parts
147
4.1.4
Prescribed Mean Curvature, Revisited
148
4.1.5
Conditions for a Local Minimum
153
4.2 Euler-Lagrange PDE
Systems
158
4.2.1
Multi-contact Geometry
159
4.2.2
Functionals on Submanifolds of Higher Codimension
163
4.2.3
The Betounes and
Poincaré-Cartan
Forms
166
4.2.4
Harmonic Maps of Riemannian Manifolds
172
4.3
Higher-Order Conservation Laws
176
4.3.1
The Infinite Prolongation
176
4.3.2
Noether s Theorem
180
4.3.3
The
К
- -1
Surface System
190
4.3.4
Two
Bäcklund
Transformations
198
|
| any_adam_object | 1 |
| author | Bryant, Robert L. 1953- Griffiths, Phillip 1938- Grossman, Daniel |
| author_GND | (DE-588)112659721 (DE-588)131881434 |
| author_facet | Bryant, Robert L. 1953- Griffiths, Phillip 1938- Grossman, Daniel |
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| ctrlnum | (OCoLC)51804819 (DE-599)BVBBV016992545 |
| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV016992545 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:12:31Z |
| institution | BVB |
| isbn | 0226077934 0226077942 |
| language | English |
| lccn | 2003044775 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010258061 |
| oclc_num | 51804819 |
| open_access_boolean | |
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| owner_facet | DE-355 DE-BY-UBR DE-824 DE-83 DE-19 DE-BY-UBM DE-384 |
| physical | VII, 213 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Univ. of Chicago Press |
| record_format | marc |
| series2 | Chicago lectures in mathematics series |
| spelling | Bryant, Robert L. 1953- Verfasser (DE-588)112659721 aut Exterior differential systems and Euler-Lagrange partial differential equations Robert Bryant, Phillip Griffiths, and Daniel Grossman Chicago [u.a.] Univ. of Chicago Press 2003 VII, 213 S. txt rdacontent n rdamedia nc rdacarrier Chicago lectures in mathematics series Análise matemática larpcal Lagrange, Équations de Pfaffianos larpcal Systèmes différentiels extérieurs Exterior differential systems Lagrange equations Äußeres Differentialsystem (DE-588)4141545-0 gnd rswk-swf Lagrange-Gleichungen (DE-588)4166461-9 gnd rswk-swf Lagrange-Gleichungen (DE-588)4166461-9 s Äußeres Differentialsystem (DE-588)4141545-0 s DE-604 Griffiths, Phillip 1938- Verfasser (DE-588)131881434 aut Grossman, Daniel Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010258061&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bryant, Robert L. 1953- Griffiths, Phillip 1938- Grossman, Daniel Exterior differential systems and Euler-Lagrange partial differential equations Análise matemática larpcal Lagrange, Équations de Pfaffianos larpcal Systèmes différentiels extérieurs Exterior differential systems Lagrange equations Äußeres Differentialsystem (DE-588)4141545-0 gnd Lagrange-Gleichungen (DE-588)4166461-9 gnd |
| subject_GND | (DE-588)4141545-0 (DE-588)4166461-9 |
| title | Exterior differential systems and Euler-Lagrange partial differential equations |
| title_auth | Exterior differential systems and Euler-Lagrange partial differential equations |
| title_exact_search | Exterior differential systems and Euler-Lagrange partial differential equations |
| title_full | Exterior differential systems and Euler-Lagrange partial differential equations Robert Bryant, Phillip Griffiths, and Daniel Grossman |
| title_fullStr | Exterior differential systems and Euler-Lagrange partial differential equations Robert Bryant, Phillip Griffiths, and Daniel Grossman |
| title_full_unstemmed | Exterior differential systems and Euler-Lagrange partial differential equations Robert Bryant, Phillip Griffiths, and Daniel Grossman |
| title_short | Exterior differential systems and Euler-Lagrange partial differential equations |
| title_sort | exterior differential systems and euler lagrange partial differential equations |
| topic | Análise matemática larpcal Lagrange, Équations de Pfaffianos larpcal Systèmes différentiels extérieurs Exterior differential systems Lagrange equations Äußeres Differentialsystem (DE-588)4141545-0 gnd Lagrange-Gleichungen (DE-588)4166461-9 gnd |
| topic_facet | Análise matemática Lagrange, Équations de Pfaffianos Systèmes différentiels extérieurs Exterior differential systems Lagrange equations Äußeres Differentialsystem Lagrange-Gleichungen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010258061&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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