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DC Field | Value | Language |
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dc.contributor.advisor | Alama, Stanley | - |
dc.contributor.advisor | Bronsard, Lia | - |
dc.contributor.author | Vriend, Silas | - |
dc.date.accessioned | 2023-05-01T14:36:28Z | - |
dc.date.available | 2023-05-01T14:36:28Z | - |
dc.date.issued | 2023 | - |
dc.identifier.uri | http://hdl.handle.net/11375/28471 | - |
dc.description.abstract | Inspired by a planar partitioning problem involving multiple unbounded chambers, this thesis investigates using classical techniques what can be said of the existence, uniqueness, and regularity of minimizers in a certain free-endpoint isoperimetric problem. In two cases, a full existence-uniqueness-regularity result is proved using a convexity technique inspired by work of Talenti. The problem studied here can be interpreted physically as the identification of the equilibrium shape of a sessile liquid drop in half-space (in the absence of gravity). This is a well-studied variational problem whose full resolution requires the use of geometric measure theory, in particular the theory of sets of finite perimeter. A crash course on the theory required for the modern statement of the equilibrium shape theorem is presented in an appendix. | en_US |
dc.language.iso | en | en_US |
dc.subject | Calculus of variations | en_US |
dc.subject | Isoperimetric problem | en_US |
dc.subject | Geometric measure theory | en_US |
dc.subject | Sets of finite perimeter | en_US |
dc.subject | Sessile drop | en_US |
dc.subject | Equilibrium shape | en_US |
dc.subject | Partitioning problem | en_US |
dc.title | On a Free-Endpoint Isoperimetric Problem | en_US |
dc.type | Thesis | en_US |
dc.contributor.department | Mathematics and Statistics | en_US |
dc.description.degreetype | Thesis | en_US |
dc.description.degree | Master of Science (MSc) | en_US |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Vriend_Silas_P_2023April_MSc.pdf | 582.6 kB | Adobe PDF | View/Open |
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