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Lipschitz Extension Problem

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dc.contributor.advisor BISWAS, ANUP en_US
dc.contributor.author GHUMMAN, MANRAJ en_US
dc.date.accessioned 2021-07-07T03:55:42Z
dc.date.available 2021-07-07T03:55:42Z
dc.date.issued 2021-06
dc.identifier.citation 88 en_US
dc.identifier.uri http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/6028
dc.description.abstract This project is mainly concerned with the understanding of the problem of extending Lipschitz functions from the boundary of some set to inside it in some special way. This extension is minimal/least fluctuating in some sense and is called the Absolutely Minimizing extension(AM). It has applications in fields like image processing and analyzing the shape of sandpiles where one can interpolate with incomplete information and fill the gaps. This is interesting from a theoretical standpoint because some of the core topics in PDE like viscosity solutions and variational methods are useful to arrive at some of the important results concerning existence and uniqueness. Interestingly, AM are viscosity solutions of the infinity Laplacian ($\Delta_{\infty}u=0)$ which is a quasilinear second-order degenerate pde. en_US
dc.description.sponsorship DST: Inspire Scholarship for Higher education en_US
dc.language.iso en en_US
dc.subject Absolute Minimizers en_US
dc.subject Infinity Laplacian en_US
dc.subject Partial Differential Equations en_US
dc.title Lipschitz Extension Problem en_US
dc.title.alternative Absolute Minimizers and the Infinity Laplacian en_US
dc.type Thesis en_US
dc.type.degree BS-MS en_US
dc.contributor.department Dept. of Mathematics en_US
dc.contributor.registration 20161057 en_US


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  • MS THESES [1705]
    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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