Direct methods in the calculus of variations:
This book provides 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 a...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2003
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| Schlagworte: | |
| Online-Zugang: | FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | This book provides 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 have been widely used in the last 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 book, 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 book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory |
| Beschreibung: | 1 Online-Ressource (vii, 403 Seiten) |
| ISBN: | 9789812795557 |
Internformat
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| 520 | |a This book provides 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 have been widely used in the last 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 book, 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 book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory | ||
| 650 | 4 | |a Calculus of variations | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Giusti, Enrico 1940-2024 |
| author_GND | (DE-588)1102399221 |
| author_facet | Giusti, Enrico 1940-2024 |
| author_role | aut |
| author_sort | Giusti, Enrico 1940-2024 |
| author_variant | e g eg |
| building | Verbundindex |
| bvnumber | BV044635706 |
| classification_rvk | SK 660 |
| collection | ZDB-124-WOP |
| ctrlnum | (ZDB-124-WOP)00003525 (OCoLC)881299031 (DE-599)BVBBV044635706 |
| 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 | Electronic eBook |
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| id | DE-604.BV044635706 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:47Z |
| institution | BVB |
| isbn | 9789812795557 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030033678 |
| oclc_num | 881299031 |
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| physical | 1 Online-Ressource (vii, 403 Seiten) |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2003 |
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| publisher | World Scientific |
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| spelling | Giusti, Enrico 1940-2024 Verfasser (DE-588)1102399221 aut Direct methods in the calculus of variations Enrico Giusti Singapore World Scientific 2003 1 Online-Ressource (vii, 403 Seiten) txt rdacontent c rdamedia cr rdacarrier This book provides 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 have been widely used in the last 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 book, 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 book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory Calculus of variations Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Direkte Methode (DE-588)4705893-6 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s Direkte Methode (DE-588)4705893-6 s DE-604 Erscheint auch als Druck-Ausgabe 9789812380432 Erscheint auch als Druck-Ausgabe 9812380434 http://www.worldscientific.com/worldscibooks/10.1142/5002#t=toc Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Giusti, Enrico 1940-2024 Direct methods in the calculus of variations Calculus of variations Variationsrechnung (DE-588)4062355-5 gnd Direkte Methode (DE-588)4705893-6 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)4705893-6 |
| title | Direct methods in the 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 | Calculus of variations Variationsrechnung (DE-588)4062355-5 gnd Direkte Methode (DE-588)4705893-6 gnd |
| topic_facet | Calculus of variations Variationsrechnung Direkte Methode |
| url | http://www.worldscientific.com/worldscibooks/10.1142/5002#t=toc |
| work_keys_str_mv | AT giustienrico directmethodsinthecalculusofvariations |