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Shape optimization and spectral theory / Antoine Henrot.

By: Material type: TextTextLanguage: English Publisher: Warsaw ; Berlin : De Gruyter Open Poland, [2017]Copyright date: ©2017Description: 1 online resourceContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783110550887
Subject(s): Additional physical formats: No title; No titleOnline resources:
Contents:
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
Summary: "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
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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

Open Access unrestricted online access star

https://purl.org/coar/access_right/c_abf2

"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

Mode of access: Internet via World Wide Web.

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

In English.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 15. Jun 2019)

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