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 |
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(CKB)3800000000210513 (DE-B1597)482667 (OCoLC)1011440073 (OCoLC)1013947651 (OCoLC)987921660 (OCoLC)992501333 (DE-B1597)9783110550887 (MiAaPQ)EBC5494961 (Au-PeEL)EBL5494961 (OCoLC)1088321323 (oapen)https://directory.doabooks.org/handle/20.500.12854/59310 (EXLCZ)993800000000210513 |
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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 |
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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, |
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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 |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
514 - Topology |
dewey-full |
514.2400000000 |
dewey-sort |
3514.2400000000 |
dewey-raw |
514.2400000000 |
dewey-search |
514.2400000000 |
oclc_num |
1011440073 1013947651 987921660 992501333 1088321323 |
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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. S. / Oudet, Edouard -- </subfield><subfield code="t">Bibliography -- </subfield><subfield code="t">Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="f">Unrestricted online access</subfield><subfield code="2">star</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Optimization.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="776" ind1=" " ind2=" "><subfield code="z">3-11-055085-7</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Girouard, Alexandre, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Henrot, Antoine, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Siudeja, Bartłomiej A., </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Helffer, Bernard, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Velichkov, Bozhidar, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Bucur, Dorin, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Oudet, Edouard, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Buttazzo, Giuseppe, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">De Philippis, Guido, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Polterovich, Iosif, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kennedy, James, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lamboley, Jimmy, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Brasco, Lorenzo, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ashbaugh, Mark S., </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pierre, Michel, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Antunes, Pedro R. 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