Semicontinuity, relaxation and integral representation in the calculus of variations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Longman
1989
|
| Edition: | 1. publ. |
| Series: | Pitman research notes in mathematics series
207 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 222 S. |
| ISBN: | 0582018595 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface and Acknowlegdments 1
Introduction 2
CHAPTER 1: Direct Method and Relaxation. The Abstract Formulation 7
1.1. Topological Generalities 7
1.2. The Direct Method 10
1.3. Relaxation 16
1.4. Some Examples 23
CHAPTER 2: Functionals Defined on LP Spaces 29
2.1. Integrands 30
2.2. Approximation of Convex Functions 38
2.3. Two Lower Semicontinuity Results 46
2.4. Integral Representation 55
2.5. A Counterexample 65
2.6. Relaxation in LP Spaces 69
2.7. Further Remarks 76
CHAPTER 3: Functionals Defined on the Space of Measures 80
3.1. Notation and Preliminary Results 81
3.2. Integral Representation 88
3.3. Relaxation in the Space of Measures 99
3.4. A Lower Semicontinuity Result 114
3.5. Some Examples 121
CHAPTER 4: Functionals Defined on Sobolev Spaces 130
4.1. Lower Semicontinuity Results 130
4.2. Lower Semicontinuity for Autonomous Functionals 136
4.3. An Integral Representation Theorem 148
4.4. Relaxation in Sobolev Spaces 156
4.5. Further Remarks 167
CHAPTER 5: Relaxation Problems in Optimal Control Theory 175
5.1. Multiple T Operators 176
5.2. The Abstract Framework 178
5.3. Problems with Ordinary State Equations 182
5.4. Problems with Elliptic State Equations 196
Bibliography 202
Index 222
|
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| id | DE-604.BV001340985 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:27:33Z |
| institution | BVB |
| isbn | 0582018595 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000811100 |
| oclc_num | 441072390 |
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| physical | 222 S. |
| publishDate | 1989 |
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| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Buttazzo, Giuseppe 1954- Verfasser (DE-588)113360568 aut Semicontinuity, relaxation and integral representation in the calculus of variations 1. publ. New York Longman 1989 222 S. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 207 Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s DE-604 Pitman research notes in mathematics series 207 (DE-604)BV000022845 207 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000811100&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buttazzo, Giuseppe 1954- Semicontinuity, relaxation and integral representation in the calculus of variations Pitman research notes in mathematics series Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4062355-5 |
| title | Semicontinuity, relaxation and integral representation in the calculus of variations |
| title_auth | Semicontinuity, relaxation and integral representation in the calculus of variations |
| title_exact_search | Semicontinuity, relaxation and integral representation in the calculus of variations |
| title_full | Semicontinuity, relaxation and integral representation in the calculus of variations |
| title_fullStr | Semicontinuity, relaxation and integral representation in the calculus of variations |
| title_full_unstemmed | Semicontinuity, relaxation and integral representation in the calculus of variations |
| title_short | Semicontinuity, relaxation and integral representation in the calculus of variations |
| title_sort | semicontinuity relaxation and integral representation in the calculus of variations |
| topic | Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Variationsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000811100&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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