東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

FindBook

Google Book

Amazon

博客來

A course in the calculus of variations = optimization, regularity, and modeling /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A course in the calculus of variations/ by Filippo Santambrogio.
其他題名:	optimization, regularity, and modeling /
作者:	Santambrogio, Filippo.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xxi, 338 p. :ill., digital ;24 cm.
內容註:	1 One-dimensional variational problems -- 2 Multi-dimensional variational problems -- 3 Lower semicontinuity -- 4 Convexity and its applications -- 5 Hölder regularity -- 6 Variational problems for sets -- 7 Γ-convergence: theory and examples.
Contained By:	Springer Nature eBook
標題:	Calculus of variations. -
電子資源:	https://doi.org/10.1007/978-3-031-45036-5
ISBN:	9783031450365

A course in the calculus of variations = optimization, regularity, and modeling /
Santambrogio, Filippo.

A course in the calculus of variationsoptimization, regularity, and modeling /[electronic resource] :by Filippo Santambrogio. - Cham :Springer International Publishing :2023. - xxi, 338 p. :ill., digital ;24 cm. - Universitext,2191-6675. - Universitext..

1 One-dimensional variational problems -- 2 Multi-dimensional variational problems -- 3 Lower semicontinuity -- 4 Convexity and its applications -- 5 Hölder regularity -- 6 Variational problems for sets -- 7 Γ-convergence: theory and examples.

This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present. Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical Hölder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality and the Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of Γ-convergence. While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.

ISBN: 9783031450365

Standard No.: 10.1007/978-3-031-45036-5doiSubjects--Topical Terms:

516604
Calculus of variations.

LC Class. No.: QA315

Dewey Class. No.: 515.64

A course in the calculus of variations = optimization, regularity, and modeling /
LDR:02796nmm a2200337 a 4500 001 2390106
003 DE-He213
005 20231217181512.0
006 m d
007 cr nn 008maaau
008 250916s2023 sz s 0 eng d
020 $a 9783031450365 $q (electronic bk.)
020 $a 9783031450358 $q (paper)
024 7 $a 10.1007/978-3-031-45036-5 $2 doi
035 $a 978-3-031-45036-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA315
072 7 $a PBU $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a PBU $2 thema
082 0 4 $a 515.64 $2 23
090 $a QA315 $b .S232 2023
100 1 $a Santambrogio, Filippo. $3 2162961
245 1 2 $a A course in the calculus of variations $h [electronic resource] : $b optimization, regularity, and modeling / $c by Filippo Santambrogio.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xxi, 338 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 2191-6675
505 0 $a 1 One-dimensional variational problems -- 2 Multi-dimensional variational problems -- 3 Lower semicontinuity -- 4 Convexity and its applications -- 5 Hölder regularity -- 6 Variational problems for sets -- 7 Γ-convergence: theory and examples.
520 $a This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present. Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical Hölder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality and the Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of Γ-convergence. While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.
650 0 $a Calculus of variations. $3 516604
650 1 4 $a Calculus of Variations and Optimization. $3 3538813
650 2 4 $a Functional Analysis. $3 893943
650 2 4 $a Differential Equations. $3 907890
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Universitext. $3 812115
856 4 0 $u https://doi.org/10.1007/978-3-031-45036-5
950 $a Mathematics and Statistics (SpringerNature-11649)