05329nam 22007335 450 991022002420332120240424225730.03-11-055088-110.1515/9783110550887(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)99380000000021051320190615d2017 fg engur|||||||||||txtrdacontentcrdamediacrrdacarrierShape optimization and spectral theory /Antoine HenrotDe Gruyter2017Warsaw ;Berlin : De Gruyter Open Poland, [2017]©20171 online resource3-11-055085-7 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"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 BozhidarMATHEMATICS / OptimizationbisacshMATHEMATICS / Optimization.514.2400000000Henrot Antoine, 503208Girouard Alexandre, ctbhttps://id.loc.gov/vocabulary/relators/ctbHenrot Antoine, ctbhttps://id.loc.gov/vocabulary/relators/ctbSiudeja Bartłomiej A., ctbhttps://id.loc.gov/vocabulary/relators/ctbHelffer Bernard, ctbhttps://id.loc.gov/vocabulary/relators/ctbVelichkov Bozhidar, ctbhttps://id.loc.gov/vocabulary/relators/ctbBucur Dorin, ctbhttps://id.loc.gov/vocabulary/relators/ctbOudet Edouard, ctbhttps://id.loc.gov/vocabulary/relators/ctbButtazzo Giuseppe, ctbhttps://id.loc.gov/vocabulary/relators/ctbDe Philippis Guido, ctbhttps://id.loc.gov/vocabulary/relators/ctbPolterovich Iosif, ctbhttps://id.loc.gov/vocabulary/relators/ctbKennedy James, ctbhttps://id.loc.gov/vocabulary/relators/ctbLamboley Jimmy, ctbhttps://id.loc.gov/vocabulary/relators/ctbBrasco Lorenzo, ctbhttps://id.loc.gov/vocabulary/relators/ctbAshbaugh Mark S., ctbhttps://id.loc.gov/vocabulary/relators/ctbPierre Michel, ctbhttps://id.loc.gov/vocabulary/relators/ctbAntunes Pedro R. S., ctbhttps://id.loc.gov/vocabulary/relators/ctbFreitas Pedro, ctbhttps://id.loc.gov/vocabulary/relators/ctbLaugesen Richard S., ctbhttps://id.loc.gov/vocabulary/relators/ctbBonnaillie-Noël Virginie, ctbhttps://id.loc.gov/vocabulary/relators/ctbDE-B1597DE-B1597BOOK9910220024203321Shape optimization and spectral theory2180578UNINA