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An investigation of capillary surfaces at non-convex corners
Mitchell, Colm Patric
Mitchell, Colm Patric
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2009-12
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In this thesis we take a close look at the paper CMC Capillary Surfaces at Reentrant Corners [33] a central feature of which is the question of when does the "central fan" of radial limits exist for a capillary graph in a vertical cylinder Ω × R ⊂ R3. The geometry of our cylinder will be examined under the condition that a non-convex (reentrant) corner P ∈ ∂Ω is present in the domain, the existence of said reentrant corner at O makes the determination of the continuity (i.e. the behavior of the radial limits at O) of the solution problematic. Given that continuity is equivalent to the existence of a "central fan" of radial limits under particular conditions, the determination of necessary and sufficient conditions for the existence of a central fan is a very important open question in the mathematical theory of capillarity.
A secondary objective is to ascertain the feasibility of certain computations to develop insight into (and perhaps conjectures about) solutions of a boundary value problem for a class of non linear elliptic partial differential equations.
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Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics
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Wichita State University