Shape Optimization : : Variations of Domains and Applications / / Catherine Bandle, Alfred Wagner.
This book investigates how domain dependent quantities from geometry and physics behave when the domain is perturbed. Of particular interest are volume- and perimeter-preserving perturbations. The first and second derivatives with respect to the perturbation are exploited for domain functionals like...
Saved in:
Superior document: | Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1 |
---|---|
VerfasserIn: | |
Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2023] ©2023 |
Year of Publication: | 2023 |
Language: | English |
Series: | De Gruyter Series in Nonlinear Analysis and Applications ,
42 |
Online Access: | |
Physical Description: | 1 online resource (XII, 280 p.) |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
9783111025438 |
---|---|
ctrlnum |
(DE-B1597)635282 |
collection |
bib_alma |
record_format |
marc |
spelling |
Bandle, Catherine, author. aut http://id.loc.gov/vocabulary/relators/aut Shape Optimization : Variations of Domains and Applications / Catherine Bandle, Alfred Wagner. Berlin ; Boston : De Gruyter, [2023] ©2023 1 online resource (XII, 280 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Series in Nonlinear Analysis and Applications , 0941-813X ; 42 Frontmatter -- Preface -- Contents -- 1 Overview of the basic problems -- 2 Basic concepts -- 3 Spherical harmonics and eigenvalue problems -- 4 Variational formulas -- 5 Geometric inequalities, convolutions, cost functions -- 6 Domain variations for energies -- 7 Discussion of the main results -- 8 General strategy and applications -- 9 Eigenvalue problems -- 10 Quantitative estimates -- 11 The Robin eigenvalues for α < 0 -- 12 Problems with infinitely many positive and negative eigenvalues -- 13 The torsion problem for α < 0 -- 14 Problems in annular domains -- 15 The first buckling eigenvalue of a clamped plate -- 16 A fourth order Steklov problem -- A General remarks -- B Geometry -- C Sobolev spaces and inequalities -- D Bilinear forms -- Notation -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star This book investigates how domain dependent quantities from geometry and physics behave when the domain is perturbed. Of particular interest are volume- and perimeter-preserving perturbations. The first and second derivatives with respect to the perturbation are exploited for domain functionals like eigenvalues, energies and geometrical quantities. They provide necessary conditions for optimal domains and are useful when global approaches like symmetrizations fail. The book is exampledriven and illustrates the usefulness of domain variations in various applications. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Aug 2023) Domänenvariation. Eigenwerte. Formoptimierung. Kugelharmonische. Störung. Shape Optimization, Domain Variation, Pertubation, Spherical Harmonics, Eigenvalues. Wagner, Alfred, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1 9783111175782 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2023 English 9783111319292 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2023 9783111318912 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2023 English 9783111319209 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2023 9783111318608 ZDB-23-DMA EPUB 9783111025810 print 9783111025261 https://doi.org/10.1515/9783111025438 https://www.degruyter.com/isbn/9783111025438 Cover https://www.degruyter.com/document/cover/isbn/9783111025438/original |
language |
English |
format |
eBook |
author |
Bandle, Catherine, Bandle, Catherine, Wagner, Alfred, |
spellingShingle |
Bandle, Catherine, Bandle, Catherine, Wagner, Alfred, Shape Optimization : Variations of Domains and Applications / De Gruyter Series in Nonlinear Analysis and Applications , Frontmatter -- Preface -- Contents -- 1 Overview of the basic problems -- 2 Basic concepts -- 3 Spherical harmonics and eigenvalue problems -- 4 Variational formulas -- 5 Geometric inequalities, convolutions, cost functions -- 6 Domain variations for energies -- 7 Discussion of the main results -- 8 General strategy and applications -- 9 Eigenvalue problems -- 10 Quantitative estimates -- 11 The Robin eigenvalues for α < 0 -- 12 Problems with infinitely many positive and negative eigenvalues -- 13 The torsion problem for α < 0 -- 14 Problems in annular domains -- 15 The first buckling eigenvalue of a clamped plate -- 16 A fourth order Steklov problem -- A General remarks -- B Geometry -- C Sobolev spaces and inequalities -- D Bilinear forms -- Notation -- Bibliography -- Index |
author_facet |
Bandle, Catherine, Bandle, Catherine, Wagner, Alfred, Wagner, Alfred, Wagner, Alfred, |
author_variant |
c b cb c b cb a w aw |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Wagner, Alfred, Wagner, Alfred, |
author2_variant |
a w aw |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Bandle, Catherine, |
title |
Shape Optimization : Variations of Domains and Applications / |
title_sub |
Variations of Domains and Applications / |
title_full |
Shape Optimization : Variations of Domains and Applications / Catherine Bandle, Alfred Wagner. |
title_fullStr |
Shape Optimization : Variations of Domains and Applications / Catherine Bandle, Alfred Wagner. |
title_full_unstemmed |
Shape Optimization : Variations of Domains and Applications / Catherine Bandle, Alfred Wagner. |
title_auth |
Shape Optimization : Variations of Domains and Applications / |
title_alt |
Frontmatter -- Preface -- Contents -- 1 Overview of the basic problems -- 2 Basic concepts -- 3 Spherical harmonics and eigenvalue problems -- 4 Variational formulas -- 5 Geometric inequalities, convolutions, cost functions -- 6 Domain variations for energies -- 7 Discussion of the main results -- 8 General strategy and applications -- 9 Eigenvalue problems -- 10 Quantitative estimates -- 11 The Robin eigenvalues for α < 0 -- 12 Problems with infinitely many positive and negative eigenvalues -- 13 The torsion problem for α < 0 -- 14 Problems in annular domains -- 15 The first buckling eigenvalue of a clamped plate -- 16 A fourth order Steklov problem -- A General remarks -- B Geometry -- C Sobolev spaces and inequalities -- D Bilinear forms -- Notation -- Bibliography -- Index |
title_new |
Shape Optimization : |
title_sort |
shape optimization : variations of domains and applications / |
series |
De Gruyter Series in Nonlinear Analysis and Applications , |
series2 |
De Gruyter Series in Nonlinear Analysis and Applications , |
publisher |
De Gruyter, |
publishDate |
2023 |
physical |
1 online resource (XII, 280 p.) Issued also in print. |
contents |
Frontmatter -- Preface -- Contents -- 1 Overview of the basic problems -- 2 Basic concepts -- 3 Spherical harmonics and eigenvalue problems -- 4 Variational formulas -- 5 Geometric inequalities, convolutions, cost functions -- 6 Domain variations for energies -- 7 Discussion of the main results -- 8 General strategy and applications -- 9 Eigenvalue problems -- 10 Quantitative estimates -- 11 The Robin eigenvalues for α < 0 -- 12 Problems with infinitely many positive and negative eigenvalues -- 13 The torsion problem for α < 0 -- 14 Problems in annular domains -- 15 The first buckling eigenvalue of a clamped plate -- 16 A fourth order Steklov problem -- A General remarks -- B Geometry -- C Sobolev spaces and inequalities -- D Bilinear forms -- Notation -- Bibliography -- Index |
isbn |
9783111025438 9783111175782 9783111319292 9783111318912 9783111319209 9783111318608 9783111025810 9783111025261 |
issn |
0941-813X ; |
url |
https://doi.org/10.1515/9783111025438 https://www.degruyter.com/isbn/9783111025438 https://www.degruyter.com/document/cover/isbn/9783111025438/original |
illustrated |
Not Illustrated |
doi_str_mv |
10.1515/9783111025438 |
work_keys_str_mv |
AT bandlecatherine shapeoptimizationvariationsofdomainsandapplications AT wagneralfred shapeoptimizationvariationsofdomainsandapplications |
status_str |
n |
ids_txt_mv |
(DE-B1597)635282 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2023 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2023 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2023 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2023 |
is_hierarchy_title |
Shape Optimization : Variations of Domains and Applications / |
container_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1 |
author2_original_writing_str_mv |
noLinkedField noLinkedField |
_version_ |
1775793046222274560 |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04631nam a22007815i 4500</leader><controlfield tag="001">9783111025438</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20230808014301.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">230808t20232023gw fo d z eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783111025438</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9783111025438</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)635282</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bandle, Catherine, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Shape Optimization :</subfield><subfield code="b">Variations of Domains and Applications /</subfield><subfield code="c">Catherine Bandle, Alfred Wagner.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin ;</subfield><subfield code="a">Boston : </subfield><subfield code="b">De Gruyter, </subfield><subfield code="c">[2023]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2023</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (XII, 280 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">De Gruyter Series in Nonlinear Analysis and Applications ,</subfield><subfield code="x">0941-813X ;</subfield><subfield code="v">42</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Preface -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">1 Overview of the basic problems -- </subfield><subfield code="t">2 Basic concepts -- </subfield><subfield code="t">3 Spherical harmonics and eigenvalue problems -- </subfield><subfield code="t">4 Variational formulas -- </subfield><subfield code="t">5 Geometric inequalities, convolutions, cost functions -- </subfield><subfield code="t">6 Domain variations for energies -- </subfield><subfield code="t">7 Discussion of the main results -- </subfield><subfield code="t">8 General strategy and applications -- </subfield><subfield code="t">9 Eigenvalue problems -- </subfield><subfield code="t">10 Quantitative estimates -- </subfield><subfield code="t">11 The Robin eigenvalues for α < 0 -- </subfield><subfield code="t">12 Problems with infinitely many positive and negative eigenvalues -- </subfield><subfield code="t">13 The torsion problem for α < 0 -- </subfield><subfield code="t">14 Problems in annular domains -- </subfield><subfield code="t">15 The first buckling eigenvalue of a clamped plate -- </subfield><subfield code="t">16 A fourth order Steklov problem -- </subfield><subfield code="t">A General remarks -- </subfield><subfield code="t">B Geometry -- </subfield><subfield code="t">C Sobolev spaces and inequalities -- </subfield><subfield code="t">D Bilinear forms -- </subfield><subfield code="t">Notation -- </subfield><subfield code="t">Bibliography -- </subfield><subfield code="t">Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book investigates how domain dependent quantities from geometry and physics behave when the domain is perturbed. Of particular interest are volume- and perimeter-preserving perturbations. The first and second derivatives with respect to the perturbation are exploited for domain functionals like eigenvalues, energies and geometrical quantities. They provide necessary conditions for optimal domains and are useful when global approaches like symmetrizations fail. The book is exampledriven and illustrates the usefulness of domain variations in various applications.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Aug 2023)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Domänenvariation.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Eigenwerte.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Formoptimierung.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Kugelharmonische.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Störung.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Shape Optimization, Domain Variation, Pertubation, Spherical Harmonics, Eigenvalues.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wagner, Alfred, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">DG Plus DeG Package 2023 Part 1</subfield><subfield code="z">9783111175782</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE COMPLETE 2023 English</subfield><subfield code="z">9783111319292</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE COMPLETE 2023</subfield><subfield code="z">9783111318912</subfield><subfield code="o">ZDB-23-DGG</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE Mathematics 2023 English</subfield><subfield code="z">9783111319209</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE Mathematics 2023</subfield><subfield code="z">9783111318608</subfield><subfield code="o">ZDB-23-DMA</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">EPUB</subfield><subfield code="z">9783111025810</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9783111025261</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9783111025438</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9783111025438</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/document/cover/isbn/9783111025438/original</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-117578-2 DG Plus DeG Package 2023 Part 1</subfield><subfield code="b">2023</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-131920-9 EBOOK PACKAGE Mathematics 2023 English</subfield><subfield code="b">2023</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-131929-2 EBOOK PACKAGE COMPLETE 2023 English</subfield><subfield code="b">2023</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_DGALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EEBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESTMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_STMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV-deGruyter-alles</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA12STME</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA13ENGE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA18STMEE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA5EBK</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield><subfield code="b">2023</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DMA</subfield><subfield code="b">2023</subfield></datafield></record></collection> |