Introduction to the calculus of variations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
New Jersey
Imperial College Press
2009
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XII, 285 S. |
| ISBN: | 9781848163331 1848163339 9781848163348 1848163347 |
Staff View
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| 240 | 1 | 0 | |a Introduction au calcul des variations |
| 245 | 1 | 0 | |a Introduction to the calculus of variations |c Bernard Dacorogna |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New Jersey |b Imperial College Press |c 2009 | |
| 300 | |a XII, 285 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Calculus of variations | |
| 650 | 4 | |a Calculus of variations | |
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Record in the Search Index
| _version_ | 1804138341731401728 |
|---|---|
| adam_text | Contents
Prefaces to the English Edition
**
Preface to the French Edition
**
0
Introduction
0.1
Brief historical comments
......................
0.2
Model problem and some examples
.................
0.3
Presentation of the content of the monograph
...........
13
1
Preliminaries
1.1
Introduction
..............................
1.2
Continuous and Holder continuous functions
1.2.1
Exercises
...........................
1.3
Lp spaces
...............................
1.3.1
Exercises
...........................
1.4
Sobolev spaces
............................
1.4.1
Exercises
...........................
1.5
Convex analysis
............................
1.5.1
Exercises
...........................
Classical methods
_
2.1
Introduction
.............................. _„
2.2
Euler-Lagrange equation
.......................
2.2.1
Exercises
...........................
2.3
Second form of the Euler-Lagrange equation
............
. .
Do
2.3.1
Exercises
......................
2.4
Hamiltonian formulation
.......................
2.4.1
Exercises
...........................
2.5
Hamilton-Jacobi equation
......................
2.5.1
Exercises
...........................
V1 CONTENTS
2.6
Fields theories
........
gì
2.6.1
Exercises
..............
gg
3
Direct methods: existence
87
3.1
Introduction
............
g7
3.2
The model case: Dirichlet integral
................. 89
3.2.1
Exercise
............................ 92
3.3
A general existence theorem
..................... 92
3.3.1
Exercises
................ 99
3.4
Euler-Lagrange equation
....................... 101
3.4.1
Exercises
................. 107
3.5
The
vectorial
case
.............. 107
3.5.1
Exercises
........................... 115
3.6
Relaxation theory
........................... 118
3.6.1
Exercises
........................... 121
4
Direct methods: regularity
125
4.1
Introduction
.............................. 125
4.2
The one dimensional case
...................... 126
4.2.1
Exercises
........................... 131
4.3
The difference quotient method: interior regularity
........ 133
4.3.1
Exercises
........................... 139
4.4
The difference quotient method: boundary regularity
....... 140
4.4.1
Exercise
............................ 143
4.5
Higher regularity for the Dirichlet integral
............. 144
4.5.1
Exercises
........................... 146
4.6
Weyl lemma
.............................. 147
4.6.1
Exercise
............................ 150
4.7
Some general results
......................... 150
4.7.1
Exercises
........................... 152
>
Minimal surfaces
155
5.1
Introduction
.............................. 155
5.2
Generalities about surfaces
..................... 158
5.2.1
Exercises
........................... 166
5.3
The Douglas-Courant-Tonelli method
................ 167
5.3.1
Exercise
............................ 173
5.4
Regularity, uniqueness and non-uniqueness
............. 173
5.5
Nonparametric minimal surfaces
.................. 175
5.5.1
Exercise
.................. 180
CONTENTS
vii
6 Isoperimetric
inequality
181
6.1
Introduction
.............................. 181
6.2
The case of dimension
2....................... 182
6.2.1
Exercises
........................... 188
6.3
The case of dimension
η
....................... 189
6.3.1
Exercises
........................... 196
7
Solutions to the Exercises
199
7.1
Chapter
1.
Preliminaries
....................... 199
7.1.1
Continuous and Holder continuous functions
....... 199
7.1.2
Lp spaces
........................... 203
7.1.3
Sobolev spaces
........................ 210
7.1.4
Convex analysis
........................ 217
7.2
Chapter
2.
Classical methods
.................... 224
7.2.1
Euler-Lagrange equation
................... 224
7.2.2
Second form of the Euler-Lagrange equation
........ 230
7.2.3
Hamiltonian formulation
................... 231
7.2.4
Hamilton-Jacobi equation
.................. 232
7.2.5
Fields theories
........................ 234
7.3
Chapter
3.
Direct methods: existence
............... 236
7.3.1
The model case: Dirichlet integral
............. 236
7.3.2
A general existence theorem
................. 236
7.3.3
Euler-Lagrange equation
................... 239
7.3.4
The
vectorial
case
...................... 240
7.3.5
Relaxation theory
...................... 247
7.4
Chapter
4.
Direct methods: regularity
............... 251
7.4.1
The one dimensional case
.................. 251
7.4.2
The difference quotient method: interior regularity
.... 254
7.4.3
The difference quotient method: boundary regularity
. . . 256
7.4.4
Higher regularity for the Dirichlet integral
......... 257
7.4.5
Weyl lemma
.......................... 259
7.4.6
Some general results
..................... 260
7.5
Chapter
5.
Minimal surfaces
..................... 263
7.5.1
Generalities about surfaces
................. 263
7.5.2
The Douglas-Courant-Tonelli method
........... 266
7.5.3
Nonparametric minimal surfaces
.............. 267
7.6
Chapter
6.
Isoperimetric inequality
................. 268
7.6.1
The case of dimension
2................... 268
7.6.2
The case of dimension
η
................... 271
Bibliography
275
|
| adam_txt |
Contents
Prefaces to the English Edition
**
Preface to the French Edition
**
0
Introduction
0.1
Brief historical comments
.
0.2
Model problem and some examples
.
0.3
Presentation of the content of the monograph
.
13
1
Preliminaries
1.1
Introduction
.
1.2
Continuous and Holder continuous functions
1.2.1
Exercises
.
1.3
Lp spaces
.
1.3.1
Exercises
.
1.4
Sobolev spaces
.
1.4.1
Exercises
.
1.5
Convex analysis
.
1.5.1
Exercises
.
Classical methods
_
2.1
Introduction
. _„
2.2
Euler-Lagrange equation
.
2.2.1
Exercises
.
2.3
Second form of the Euler-Lagrange equation
.
. .
Do
2.3.1
Exercises
.
2.4
Hamiltonian formulation
.
2.4.1
Exercises
.
2.5
Hamilton-Jacobi equation
.
2.5.1
Exercises
.
V1 CONTENTS
2.6
Fields theories
.
gì
2.6.1
Exercises
.
gg
3
Direct methods: existence
87
3.1
Introduction
.
g7
3.2
The model case: Dirichlet integral
. 89
3.2.1
Exercise
. 92
3.3
A general existence theorem
. 92
3.3.1
Exercises
. 99
3.4
Euler-Lagrange equation
. 101
3.4.1
Exercises
. 107
3.5
The
vectorial
case
. 107
3.5.1
Exercises
. 115
3.6
Relaxation theory
. 118
3.6.1
Exercises
. 121
4
Direct methods: regularity
125
4.1
Introduction
. 125
4.2
The one dimensional case
. 126
4.2.1
Exercises
. 131
4.3
The difference quotient method: interior regularity
. 133
4.3.1
Exercises
. 139
4.4
The difference quotient method: boundary regularity
. 140
4.4.1
Exercise
. 143
4.5
Higher regularity for the Dirichlet integral
. 144
4.5.1
Exercises
. 146
4.6
Weyl lemma
. 147
4.6.1
Exercise
. 150
4.7
Some general results
. 150
4.7.1
Exercises
. 152
>
Minimal surfaces
155
5.1
Introduction
. 155
5.2
Generalities about surfaces
. 158
5.2.1
Exercises
. 166
5.3
The Douglas-Courant-Tonelli method
. 167
5.3.1
Exercise
. 173
5.4
Regularity, uniqueness and non-uniqueness
. 173
5.5
Nonparametric minimal surfaces
. 175
5.5.1
Exercise
. 180
CONTENTS
vii
6 Isoperimetric
inequality
181
6.1
Introduction
. 181
6.2
The case of dimension
2. 182
6.2.1
Exercises
. 188
6.3
The case of dimension
η
. 189
6.3.1
Exercises
. 196
7
Solutions to the Exercises
199
7.1
Chapter
1.
Preliminaries
. 199
7.1.1
Continuous and Holder continuous functions
. 199
7.1.2
Lp spaces
. 203
7.1.3
Sobolev spaces
. 210
7.1.4
Convex analysis
. 217
7.2
Chapter
2.
Classical methods
. 224
7.2.1
Euler-Lagrange equation
. 224
7.2.2
Second form of the Euler-Lagrange equation
. 230
7.2.3
Hamiltonian formulation
. 231
7.2.4
Hamilton-Jacobi equation
. 232
7.2.5
Fields theories
. 234
7.3
Chapter
3.
Direct methods: existence
. 236
7.3.1
The model case: Dirichlet integral
. 236
7.3.2
A general existence theorem
. 236
7.3.3
Euler-Lagrange equation
. 239
7.3.4
The
vectorial
case
. 240
7.3.5
Relaxation theory
. 247
7.4
Chapter
4.
Direct methods: regularity
. 251
7.4.1
The one dimensional case
. 251
7.4.2
The difference quotient method: interior regularity
. 254
7.4.3
The difference quotient method: boundary regularity
. . . 256
7.4.4
Higher regularity for the Dirichlet integral
. 257
7.4.5
Weyl lemma
. 259
7.4.6
Some general results
. 260
7.5
Chapter
5.
Minimal surfaces
. 263
7.5.1
Generalities about surfaces
. 263
7.5.2
The Douglas-Courant-Tonelli method
. 266
7.5.3
Nonparametric minimal surfaces
. 267
7.6
Chapter
6.
Isoperimetric inequality
. 268
7.6.1
The case of dimension
2. 268
7.6.2
The case of dimension
η
. 271
Bibliography
275 |
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| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515 264 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035172865 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:55:00Z |
| indexdate | 2024-07-09T21:26:39Z |
| institution | BVB |
| isbn | 9781848163331 1848163339 9781848163348 1848163347 |
| language | English French |
| lccn | 2008038721 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016979779 |
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| physical | XII, 285 S. |
| publishDate | 2009 |
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| publisher | Imperial College Press |
| record_format | marc |
| spelling | Dacorogna, Bernard 1953- Verfasser (DE-588)133791920 aut Introduction au calcul des variations Introduction to the calculus of variations Bernard Dacorogna 2. ed. New Jersey Imperial College Press 2009 XII, 285 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Calculus of variations Variationsrechnung (DE-588)4062355-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Variationsrechnung (DE-588)4062355-5 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016979779&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dacorogna, Bernard 1953- Introduction to the calculus of variations Calculus of variations Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)4123623-3 |
| title | Introduction to the calculus of variations |
| title_alt | Introduction au calcul des variations |
| title_auth | Introduction to the calculus of variations |
| title_exact_search | Introduction to the calculus of variations |
| title_exact_search_txtP | Introduction to the calculus of variations |
| title_full | Introduction to the calculus of variations Bernard Dacorogna |
| title_fullStr | Introduction to the calculus of variations Bernard Dacorogna |
| title_full_unstemmed | Introduction to the calculus of variations Bernard Dacorogna |
| title_short | Introduction to the calculus of variations |
| title_sort | introduction to the calculus of variations |
| topic | Calculus of variations Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Calculus of variations Variationsrechnung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016979779&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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