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
Physical Description:1 online resource
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100 1 |a Henrot, Antoine,   |e author. 
245 1 0 |a Shape optimization and spectral theory /  |c Antoine Henrot. 
260 |b De Gruyter  |c 2017 
264 1 |a Warsaw ;  |a Berlin :   |b De Gruyter Open Poland,   |c [2017] 
264 4 |c ©2017 
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588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 15. Jun 2019) 
540 |a This eBook is made available Open Access under a CC BY-NC-ND 4.0 license:   |u https://creativecommons.org/licenses/by-nc-nd/4.0   |u https://www.degruyter.com/dg/page/open-access-policy 
520 |a "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 
546 |a In English. 
505 0 0 |t Frontmatter --   |t Contents --   |t 1 Introduction /   |r Henrot, Antoine --   |t 2 Existence results /   |r Bucur, Dorin --   |t 3 Regularity of optimal spectral domains /   |r Lamboley, Jimmy / Pierre, Michel --   |t 4 The Robin problem /   |r Bucur, Dorin / Freitas, Pedro / Kennedy, James --   |t 5 Spectral geometry of the Steklov problem /   |r Girouard, Alexandre / Polterovich, Iosif --   |t 6 Triangles and Other Special Domains /   |r Laugesen, Richard S. / Siudeja, Bartłomiej A. --   |t 7 Spectral inequalities in quantitative form /   |r Brasco, Lorenzo / De Philippis, Guido --   |t 8 Universal Inequalities for the Eigenvalues of the Dirichlet Laplacian /   |r Ashbaugh, Mark S. --   |t 9 Spectral optimization problems for Schrödinger operators /   |r Buttazzo, Giuseppe / Velichkov, Bozhidar --   |t 10 Nodal and spectral minimal partitions - The state of the art in 2016 - /   |r Bonnaillie-Noël, Virginie / Helffer, Bernard --   |t 11 Numerical results for extremal problem for eigenvalues of the Laplacian /   |r Antunes, Pedro R. S. / Oudet, Edouard --   |t Bibliography --   |t Index 
506 0 |f Unrestricted online access  |2 star 
650 7 |a MATHEMATICS / Optimization.  |2 bisacsh 
776 |z 3-11-055085-7 
700 1 |a Girouard, Alexandre,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Henrot, Antoine,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Siudeja, Bartłomiej A.,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Helffer, Bernard,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Velichkov, Bozhidar,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Bucur, Dorin,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Oudet, Edouard,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Buttazzo, Giuseppe,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a De Philippis, Guido,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Polterovich, Iosif,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Kennedy, James,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Lamboley, Jimmy,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Brasco, Lorenzo,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Ashbaugh, Mark S.,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Pierre, Michel,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Antunes, Pedro R. S.,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Freitas, Pedro,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Laugesen, Richard S.,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
700 1 |a Bonnaillie-Noël, Virginie,   |e contributor.  |4 ctb  |4 https://id.loc.gov/vocabulary/relators/ctb 
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