LEADER 05329nam 22007335 450 001 9910220024203321 005 20240424225730.0 010 $a3-11-055088-1 024 7 $a10.1515/9783110550887 035 $a(CKB)3800000000210513 035 $a(DE-B1597)482667 035 $a(OCoLC)1011440073 035 $a(OCoLC)1013947651 035 $a(OCoLC)987921660 035 $a(OCoLC)992501333 035 $a(DE-B1597)9783110550887 035 $a(MiAaPQ)EBC5494961 035 $a(Au-PeEL)EBL5494961 035 $a(OCoLC)1088321323 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/59310 035 $a(EXLCZ)993800000000210513 100 $a20190615d2017 fg 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aShape optimization and spectral theory /$fAntoine Henrot 210 $cDe Gruyter$d2017 210 1$aWarsaw ;$aBerlin : $cDe Gruyter Open Poland, $d[2017] 210 4$d©2017 215 $a1 online resource 311 $a3-11-055085-7 327 $tFrontmatter -- $tContents -- $t1 Introduction / $rHenrot, Antoine -- $t2 Existence results / $rBucur, Dorin -- $t3 Regularity of optimal spectral domains / $rLamboley, Jimmy / Pierre, Michel -- $t4 The Robin problem / $rBucur, Dorin / Freitas, Pedro / Kennedy, James -- $t5 Spectral geometry of the Steklov problem / $rGirouard, Alexandre / Polterovich, Iosif -- $t6 Triangles and Other Special Domains / $rLaugesen, Richard S. / Siudeja, Bart?omiej A. -- $t7 Spectral inequalities in quantitative form / $rBrasco, Lorenzo / De Philippis, Guido -- $t8 Universal Inequalities for the Eigenvalues of the Dirichlet Laplacian / $rAshbaugh, Mark S. -- $t9 Spectral optimization problems for Schrödinger operators / $rButtazzo, Giuseppe / Velichkov, Bozhidar -- $t10 Nodal and spectral minimal partitions - The state of the art in 2016 - / $rBonnaillie-Noël, Virginie / Helffer, Bernard -- $t11 Numerical results for extremal problem for eigenvalues of the Laplacian / $rAntunes, Pedro R. S. / Oudet, Edouard -- $tBibliography -- $tIndex 330 $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 Bart?omiej A., Velichkov Bozhidar 606 $aMATHEMATICS / Optimization$2bisacsh 615 7$aMATHEMATICS / Optimization. 676 $a514.2400000000 700 $aHenrot$b Antoine, $0503208 702 $aGirouard$b Alexandre, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aHenrot$b Antoine, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aSiudeja$b Bart?omiej A., $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aHelffer$b Bernard, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aVelichkov$b Bozhidar, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aBucur$b Dorin, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aOudet$b Edouard, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aButtazzo$b Giuseppe, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aDe Philippis$b Guido, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aPolterovich$b Iosif, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aKennedy$b James, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aLamboley$b Jimmy, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aBrasco$b Lorenzo, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aAshbaugh$b Mark S., $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aPierre$b Michel, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aAntunes$b Pedro R. S., $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aFreitas$b Pedro, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aLaugesen$b Richard S., $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 702 $aBonnaillie-Noël$b Virginie, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910220024203321 996 $aShape optimization and spectral theory$92180578 997 $aUNINA