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Please use this identifier to cite or link to this item: 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

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