Direct methods in the calculus of variations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New Jersey
World Scientific
2005
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| Subjects: | |
| Online Access: | FAW01 FAW02 UER01 Volltext |
| Item Description: | Includes bibliographical references (pages 377-398) and index A comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well-known and were widely-used in the 20th century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this work, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The volume is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory |
| Physical Description: | 1 Online-Ressource (vii, 403 pages) |
| ISBN: | 1281935905 9781281935908 9789812795557 9812795553 |
Staff View
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| 100 | 1 | |a Giusti, Enrico |d 1940-2024 |e Verfasser |0 (DE-588)1102399221 |4 aut | |
| 245 | 1 | 0 | |a Direct methods in the calculus of variations |c Enrico Giusti |
| 246 | 1 | 3 | |a Calculus of variations |
| 264 | 1 | |a New Jersey |b World Scientific |c 2005 | |
| 300 | |a 1 Online-Ressource (vii, 403 pages) | ||
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| 500 | |a Includes bibliographical references (pages 377-398) and index | ||
| 500 | |a A comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well-known and were widely-used in the 20th century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this work, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The volume is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory | ||
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| author | Giusti, Enrico 1940-2024 |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| isbn | 1281935905 9781281935908 9789812795557 9812795553 |
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| spelling | Giusti, Enrico 1940-2024 Verfasser (DE-588)1102399221 aut Direct methods in the calculus of variations Enrico Giusti Calculus of variations New Jersey World Scientific 2005 1 Online-Ressource (vii, 403 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 377-398) and index A comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well-known and were widely-used in the 20th century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this work, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The volume is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Calculus of variations fast Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235657 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Giusti, Enrico 1940-2024 Direct methods in the calculus of variations MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Calculus of variations fast Calculus of variations Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4062355-5 |
| title | Direct methods in the calculus of variations |
| title_alt | Calculus of variations |
| title_auth | Direct methods in the calculus of variations |
| title_exact_search | Direct methods in the calculus of variations |
| title_full | Direct methods in the calculus of variations Enrico Giusti |
| title_fullStr | Direct methods in the calculus of variations Enrico Giusti |
| title_full_unstemmed | Direct methods in the calculus of variations Enrico Giusti |
| title_short | Direct methods in the calculus of variations |
| title_sort | direct methods in the calculus of variations |
| topic | MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Calculus of variations fast Calculus of variations Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Calculus of variations Variationsrechnung |
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