Shape optimization and spectral theory / / Antoine Henrot.

"Shape optimization and spectral theory" is a survey book aiming to give an overview of recent results in spectral geometry and its links with shape optimization.It covers most of the issues which are important for people working in PDE and differential geometry interested in sharp inequal...

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Place / Publishing House:Warsaw ;, Berlin : : De Gruyter Open Poland, , [2017]
©2017
Year of Publication:2017
Language:English
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spelling Henrot, Antoine, author.
Shape optimization and spectral theory / Antoine Henrot.
De Gruyter 2017
Warsaw ; Berlin : De Gruyter Open Poland, [2017]
©2017
1 online resource
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Description based on online resource; title from PDF title page (publisher's Web site, viewed 15. Jun 2019)
This eBook is made available Open Access under a CC BY-NC-ND 4.0 license: https://creativecommons.org/licenses/by-nc-nd/4.0 https://www.degruyter.com/dg/page/open-access-policy
"Shape optimization and spectral theory" is a survey book aiming to give an overview of recent results in spectral geometry and its links with shape optimization.It covers most of the issues which are important for people working in PDE and differential geometry interested in sharp inequalities and qualitative behaviour for eigenvalues of the Laplacian with different kind of boundary conditions (Dirichlet, Robin and Steklov). This includes: existence of optimal shapes, their regularity, the case of special domains like triangles, isospectrality, quantitative form of the isoperimetric inequalities, optimal partitions, universal inequalities and numerical results.Much progress has been made in these extremum problems during the last ten years and this edited volume presents a valuable update to a wide community interested in these topics. List of contributorsAntunes Pedro R.S., Ashbaugh Mark, Bonnaillie-Noël Virginie, Brasco Lorenzo, Bucur Dorin, Buttazzo Giuseppe, De Philippis Guido, Freitas Pedro, Girouard Alexandre, Helffer Bernard, Kennedy James, Lamboley Jimmy, Laugesen Richard S., Oudet Edouard, Pierre Michel, Polterovich Iosif, Siudeja Bartłomiej A., Velichkov Bozhidar
In English.
Frontmatter -- Contents -- 1 Introduction / Henrot, Antoine -- 2 Existence results / Bucur, Dorin -- 3 Regularity of optimal spectral domains / Lamboley, Jimmy / Pierre, Michel -- 4 The Robin problem / Bucur, Dorin / Freitas, Pedro / Kennedy, James -- 5 Spectral geometry of the Steklov problem / Girouard, Alexandre / Polterovich, Iosif -- 6 Triangles and Other Special Domains / Laugesen, Richard S. / Siudeja, Bartłomiej A. -- 7 Spectral inequalities in quantitative form / Brasco, Lorenzo / De Philippis, Guido -- 8 Universal Inequalities for the Eigenvalues of the Dirichlet Laplacian / Ashbaugh, Mark S. -- 9 Spectral optimization problems for Schrödinger operators / Buttazzo, Giuseppe / Velichkov, Bozhidar -- 10 Nodal and spectral minimal partitions - The state of the art in 2016 - / Bonnaillie-Noël, Virginie / Helffer, Bernard -- 11 Numerical results for extremal problem for eigenvalues of the Laplacian / Antunes, Pedro R. S. / Oudet, Edouard -- Bibliography -- Index
Unrestricted online access star
MATHEMATICS / Optimization. bisacsh
3-11-055085-7
Girouard, Alexandre, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Henrot, Antoine, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Siudeja, Bartłomiej A., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Helffer, Bernard, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Velichkov, Bozhidar, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Bucur, Dorin, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Oudet, Edouard, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Buttazzo, Giuseppe, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
De Philippis, Guido, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Polterovich, Iosif, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Kennedy, James, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Lamboley, Jimmy, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Brasco, Lorenzo, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Ashbaugh, Mark S., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Pierre, Michel, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Antunes, Pedro R. S., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Freitas, Pedro, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Laugesen, Richard S., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Bonnaillie-Noël, Virginie, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
language English
format eBook
author Henrot, Antoine,
spellingShingle Henrot, Antoine,
Shape optimization and spectral theory /
Frontmatter --
Contents --
1 Introduction /
2 Existence results /
3 Regularity of optimal spectral domains /
4 The Robin problem /
5 Spectral geometry of the Steklov problem /
6 Triangles and Other Special Domains /
7 Spectral inequalities in quantitative form /
8 Universal Inequalities for the Eigenvalues of the Dirichlet Laplacian /
9 Spectral optimization problems for Schrödinger operators /
10 Nodal and spectral minimal partitions - The state of the art in 2016 - /
11 Numerical results for extremal problem for eigenvalues of the Laplacian /
Bibliography --
Index
author_facet Henrot, Antoine,
Girouard, Alexandre,
Girouard, Alexandre,
Henrot, Antoine,
Henrot, Antoine,
Siudeja, Bartłomiej A.,
Siudeja, Bartłomiej A.,
Helffer, Bernard,
Helffer, Bernard,
Velichkov, Bozhidar,
Velichkov, Bozhidar,
Bucur, Dorin,
Bucur, Dorin,
Oudet, Edouard,
Oudet, Edouard,
Buttazzo, Giuseppe,
Buttazzo, Giuseppe,
De Philippis, Guido,
De Philippis, Guido,
Polterovich, Iosif,
Polterovich, Iosif,
Kennedy, James,
Kennedy, James,
Lamboley, Jimmy,
Lamboley, Jimmy,
Brasco, Lorenzo,
Brasco, Lorenzo,
Ashbaugh, Mark S.,
Ashbaugh, Mark S.,
Pierre, Michel,
Pierre, Michel,
Antunes, Pedro R. S.,
Antunes, Pedro R. S.,
Freitas, Pedro,
Freitas, Pedro,
Laugesen, Richard S.,
Laugesen, Richard S.,
Bonnaillie-Noël, Virginie,
Bonnaillie-Noël, Virginie,
author_variant a h ah
author_role VerfasserIn
author2 Girouard, Alexandre,
Girouard, Alexandre,
Henrot, Antoine,
Henrot, Antoine,
Siudeja, Bartłomiej A.,
Siudeja, Bartłomiej A.,
Helffer, Bernard,
Helffer, Bernard,
Velichkov, Bozhidar,
Velichkov, Bozhidar,
Bucur, Dorin,
Bucur, Dorin,
Oudet, Edouard,
Oudet, Edouard,
Buttazzo, Giuseppe,
Buttazzo, Giuseppe,
De Philippis, Guido,
De Philippis, Guido,
Polterovich, Iosif,
Polterovich, Iosif,
Kennedy, James,
Kennedy, James,
Lamboley, Jimmy,
Lamboley, Jimmy,
Brasco, Lorenzo,
Brasco, Lorenzo,
Ashbaugh, Mark S.,
Ashbaugh, Mark S.,
Pierre, Michel,
Pierre, Michel,
Antunes, Pedro R. S.,
Antunes, Pedro R. S.,
Freitas, Pedro,
Freitas, Pedro,
Laugesen, Richard S.,
Laugesen, Richard S.,
Bonnaillie-Noël, Virginie,
Bonnaillie-Noël, Virginie,
author2_variant a g ag
a g ag
a h ah
a h ah
b a s ba bas
b a s ba bas
b h bh
b h bh
b v bv
b v bv
d b db
d b db
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p g d pg pgd
p g d pg pgd
i p ip
i p ip
j k jk
j k jk
j l jl
j l jl
l b lb
l b lb
m s a ms msa
m s a ms msa
m p mp
m p mp
p r s a prs prsa
p r s a prs prsa
p f pf
p f pf
r s l rs rsl
r s l rs rsl
v b n vbn
v b n vbn
author2_role MitwirkendeR
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MitwirkendeR
MitwirkendeR
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MitwirkendeR
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MitwirkendeR
MitwirkendeR
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MitwirkendeR
MitwirkendeR
author_sort Henrot, Antoine,
author_additional Henrot, Antoine --
Bucur, Dorin --
Lamboley, Jimmy / Pierre, Michel --
Bucur, Dorin / Freitas, Pedro / Kennedy, James --
Girouard, Alexandre / Polterovich, Iosif --
Laugesen, Richard S. / Siudeja, Bartłomiej A. --
Brasco, Lorenzo / De Philippis, Guido --
Ashbaugh, Mark S. --
Buttazzo, Giuseppe / Velichkov, Bozhidar --
Bonnaillie-Noël, Virginie / Helffer, Bernard --
Antunes, Pedro R. S. / Oudet, Edouard --
title Shape optimization and spectral theory /
title_full Shape optimization and spectral theory / Antoine Henrot.
title_fullStr Shape optimization and spectral theory / Antoine Henrot.
title_full_unstemmed Shape optimization and spectral theory / Antoine Henrot.
title_auth Shape optimization and spectral theory /
title_alt Frontmatter --
Contents --
1 Introduction /
2 Existence results /
3 Regularity of optimal spectral domains /
4 The Robin problem /
5 Spectral geometry of the Steklov problem /
6 Triangles and Other Special Domains /
7 Spectral inequalities in quantitative form /
8 Universal Inequalities for the Eigenvalues of the Dirichlet Laplacian /
9 Spectral optimization problems for Schrödinger operators /
10 Nodal and spectral minimal partitions - The state of the art in 2016 - /
11 Numerical results for extremal problem for eigenvalues of the Laplacian /
Bibliography --
Index
title_new Shape optimization and spectral theory /
title_sort shape optimization and spectral theory /
publisher De Gruyter
De Gruyter Open Poland,
publishDate 2017
physical 1 online resource
contents Frontmatter --
Contents --
1 Introduction /
2 Existence results /
3 Regularity of optimal spectral domains /
4 The Robin problem /
5 Spectral geometry of the Steklov problem /
6 Triangles and Other Special Domains /
7 Spectral inequalities in quantitative form /
8 Universal Inequalities for the Eigenvalues of the Dirichlet Laplacian /
9 Spectral optimization problems for Schrödinger operators /
10 Nodal and spectral minimal partitions - The state of the art in 2016 - /
11 Numerical results for extremal problem for eigenvalues of the Laplacian /
Bibliography --
Index
isbn 3-11-055088-1
3-11-055085-7
callnumber-first Q - Science
callnumber-subject QA - Mathematics
callnumber-label QA564
callnumber-sort QA 3564 S4527 42017
illustrated Not Illustrated
oclc_num 1011440073
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This includes: existence of optimal shapes, their regularity, the case of special domains like triangles, isospectrality, quantitative form of the isoperimetric inequalities, optimal partitions, universal inequalities and numerical results.Much progress has been made in these extremum problems during the last ten years and this edited volume presents a valuable update to a wide community interested in these topics. List of contributorsAntunes Pedro R.S., Ashbaugh Mark, Bonnaillie-Noël Virginie, Brasco Lorenzo, Bucur Dorin, Buttazzo Giuseppe, De Philippis Guido, Freitas Pedro, Girouard Alexandre, Helffer Bernard, Kennedy James, Lamboley Jimmy, Laugesen Richard S., Oudet Edouard, Pierre Michel, Polterovich Iosif, Siudeja Bartłomiej A., Velichkov Bozhidar</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">1 Introduction / </subfield><subfield code="r">Henrot, Antoine -- </subfield><subfield code="t">2 Existence results / </subfield><subfield code="r">Bucur, Dorin -- </subfield><subfield code="t">3 Regularity of optimal spectral domains / </subfield><subfield code="r">Lamboley, Jimmy / Pierre, Michel -- </subfield><subfield code="t">4 The Robin problem / </subfield><subfield code="r">Bucur, Dorin / Freitas, Pedro / Kennedy, James -- </subfield><subfield code="t">5 Spectral geometry of the Steklov problem / </subfield><subfield code="r">Girouard, Alexandre / Polterovich, Iosif -- </subfield><subfield code="t">6 Triangles and Other Special Domains / </subfield><subfield code="r">Laugesen, Richard S. / Siudeja, Bartłomiej A. -- </subfield><subfield code="t">7 Spectral inequalities in quantitative form / </subfield><subfield code="r">Brasco, Lorenzo / De Philippis, Guido -- </subfield><subfield code="t">8 Universal Inequalities for the Eigenvalues of the Dirichlet Laplacian / </subfield><subfield code="r">Ashbaugh, Mark S. -- </subfield><subfield code="t">9 Spectral optimization problems for Schrödinger operators / </subfield><subfield code="r">Buttazzo, Giuseppe / Velichkov, Bozhidar -- </subfield><subfield code="t">10 Nodal and spectral minimal partitions - The state of the art in 2016 - / </subfield><subfield code="r">Bonnaillie-Noël, Virginie / Helffer, Bernard -- </subfield><subfield code="t">11 Numerical results for extremal problem for eigenvalues of the Laplacian / </subfield><subfield code="r">Antunes, Pedro R. 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