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http://hdl.handle.net/11375/28471
Title: | On a Free-Endpoint Isoperimetric Problem |
Authors: | Vriend, Silas |
Advisor: | Alama, Stanley Bronsard, Lia |
Department: | Mathematics and Statistics |
Keywords: | Calculus of variations;Isoperimetric problem;Geometric measure theory;Sets of finite perimeter;Sessile drop;Equilibrium shape;Partitioning problem |
Publication Date: | 2023 |
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. |
URI: | http://hdl.handle.net/11375/28471 |
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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