One-dimensional variational problems: an introduction
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon
1998
|
| Series: | Oxford lecture series in mathematics and its applications
15 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | VIII, 262 S. graph. Darst. |
| ISBN: | 0198504659 |
Staff View
MARC
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| 245 | 1 | 0 | |a One-dimensional variational problems |b an introduction |c Giuseppe Buttazzo and Mariano Giaquinta and Stefan Hildebrandt |
| 246 | 1 | 3 | |a One dimensional variational problems |
| 264 | 1 | |a Oxford |b Clarendon |c 1998 | |
| 300 | |a VIII, 262 S. |b graph. Darst. | ||
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| 700 | 1 | |a Hildebrandt, Stefan |d 1936-2015 |e Verfasser |0 (DE-588)119219050 |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Introduction 1
1 Classical problems and indirect methods 10
1.1 The Euler equation and other necessary conditions for optimality 10
1.2 Calibrators and sufficient conditions for minima 25
1.3 Some classical problems 39
2 Absolutely continuous functions and Sobolev spaces 54
2.1 Sobolev spaces in dimension 1 54
2.2 Absolutely continuous functions 80
2.3 Functions of bounded variation 90
3 Semicontinuity and existence results 104
3.1 A lower semicontinuity theorem 104
3.2 Existence results in Sobolev spaces 114
3.3 Lower semicontinuity in the space of measures 124
3.4 Existence results in the space BV 128
4 Regularity of minimizers 134
4.1 The regular case 134
4.2 Tonelli s partial regularity theorem 139
4.3 The Lavrentiev phenomenon and the singular set 146
5 Some applications 156
5.1 Boundary value problems 156
5.2 The Sturm Liouville eigenvalue problem 163
5.3 The vibrating string 184
5.4 Variational problems with obstacles 187
5.5 Periodic solutions of variational problems 193
5.6 Periodic solutions of Hamiltonian systems 199
5.7 Non coercive variational problems 203
5.8 An existence result in optimal control theory 211
5.9 Parametric variational problems 216
6 Scholia 225
6.1 Additional remarks on the calculus of variations 225
6.2 Semicontinuity and compactness 226
6.3 Absolutely continuous functions 228
6.4 Sobolev spaces 230
6.5 Non convex functionals on measures and bounded variation
functions 231
6.6 Direct methods 232
viii Contents
6.7 Lavrentiev phenomenon 235
6.8 The vibrating string problem 242
6.9 Variational inequalities and the obstacle problem. Non coercive
problems 244
6.10 Periodic solutions 244
References 246
Index 261
|
| any_adam_object | 1 |
| author | Buttazzo, Giuseppe 1954- Giaquinta, Mariano 1947- Hildebrandt, Stefan 1936-2015 |
| author_GND | (DE-588)113360568 (DE-588)111595738 (DE-588)119219050 |
| author_facet | Buttazzo, Giuseppe 1954- Giaquinta, Mariano 1947- Hildebrandt, Stefan 1936-2015 |
| author_role | aut aut aut |
| author_sort | Buttazzo, Giuseppe 1954- |
| author_variant | g b gb m g mg s h sh |
| building | Verbundindex |
| bvnumber | BV012511996 |
| classification_rvk | SK 660 |
| classification_tum | MAT 490f |
| ctrlnum | (OCoLC)264111190 (DE-599)BVBBV012511996 |
| dewey-full | 515.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.64 |
| dewey-search | 515.64 |
| dewey-sort | 3515.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012511996 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:28:51Z |
| institution | BVB |
| isbn | 0198504659 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008492437 |
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| physical | VIII, 262 S. graph. Darst. |
| publishDate | 1998 |
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| publisher | Clarendon |
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| series | Oxford lecture series in mathematics and its applications |
| series2 | Oxford lecture series in mathematics and its applications Oxford science publications |
| spelling | Buttazzo, Giuseppe 1954- Verfasser (DE-588)113360568 aut One-dimensional variational problems an introduction Giuseppe Buttazzo and Mariano Giaquinta and Stefan Hildebrandt One dimensional variational problems Oxford Clarendon 1998 VIII, 262 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford lecture series in mathematics and its applications 15 Oxford science publications Hier auch später erschienene, unveränderte Nachdrucke Calculus of variations Variationsproblem (DE-588)4187419-5 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Variationsproblem (DE-588)4187419-5 s DE-604 Variationsrechnung (DE-588)4062355-5 s Giaquinta, Mariano 1947- Verfasser (DE-588)111595738 aut Hildebrandt, Stefan 1936-2015 Verfasser (DE-588)119219050 aut Oxford lecture series in mathematics and its applications 15 (DE-604)BV009910017 15 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008492437&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buttazzo, Giuseppe 1954- Giaquinta, Mariano 1947- Hildebrandt, Stefan 1936-2015 One-dimensional variational problems an introduction Oxford lecture series in mathematics and its applications Calculus of variations Variationsproblem (DE-588)4187419-5 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4187419-5 (DE-588)4062355-5 |
| title | One-dimensional variational problems an introduction |
| title_alt | One dimensional variational problems |
| title_auth | One-dimensional variational problems an introduction |
| title_exact_search | One-dimensional variational problems an introduction |
| title_full | One-dimensional variational problems an introduction Giuseppe Buttazzo and Mariano Giaquinta and Stefan Hildebrandt |
| title_fullStr | One-dimensional variational problems an introduction Giuseppe Buttazzo and Mariano Giaquinta and Stefan Hildebrandt |
| title_full_unstemmed | One-dimensional variational problems an introduction Giuseppe Buttazzo and Mariano Giaquinta and Stefan Hildebrandt |
| title_short | One-dimensional variational problems |
| title_sort | one dimensional variational problems an introduction |
| title_sub | an introduction |
| topic | Calculus of variations Variationsproblem (DE-588)4187419-5 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Calculus of variations Variationsproblem Variationsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008492437&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009910017 |
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