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Shape Optimization Problems on Polygons

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dc.contributor.advisor Verma, Sheela
dc.contributor.advisor CHORWADWALA, ANISA
dc.contributor.author V, SRIRAM
dc.date.accessioned 2024-05-15T09:06:46Z
dc.date.available 2024-05-15T09:06:46Z
dc.date.issued 2024-05
dc.identifier.citation 116 en_US
dc.identifier.uri http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8777
dc.description.abstract In this thesis, we aim to study the Polya -Szego conjecture, which states that the regular polygon with n sides and fixed area minimizes the first Dirichlet eigenvalue among the family of simple polygons with $n$ sides in R^2 and fixed area for n greater than or equal to 3. The conjecture for the cases n = 3,4 was solved using Steiner symmetrization . However, Steiner symmetrization fails to prove the conjecture when we consider n is greater than or equal to 5. In 2022, Beniamin Bogosel and Dorin Bucur showed that the proof of the conjecture for n greater than or equal to 5 can be reduced to a finite number of numerical computations, assuming that the conjecture is true. They used the theory of shape derivatives and the finite element method to prove the local minimality of the regular polygon with a fixed area. They use surgery arguments further to prove the global minimality of the regular polygon with a fixed area. en_US
dc.language.iso en en_US
dc.subject Mathematics en_US
dc.title Shape Optimization Problems on Polygons en_US
dc.type Thesis en_US
dc.description.embargo One Year en_US
dc.type.degree BS-MS en_US
dc.contributor.department Dept. of Mathematics en_US
dc.contributor.registration 20191014 en_US


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  • MS THESES [1713]
    Thesis submitted to IISER Pune in partial fulfilment of the requirements for the BS-MS Dual Degree Programme/MSc. Programme/MS-Exit Programme

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