Electron. J. Differential Equations, Vol. 2023 (2023), No. 32, pp. 1-11.

Discussion of a uniqueness result in ``Equilibrium Configurations for a Floating Drop''

Raymond Treinen

We analyze a uniqueness result presented by Elcrat, Neel, and Siegel [1] for unbounded liquid bridges, and show that the proof they presented is incorrect. We add a hypothesis to their stated theorem and prove that their result holds under this condition. Then we use Chebyshev spectral methods to approximate solutions to certain boundary value problems used to check this hypothesis holds at least on a range of cases.

Submitted July 22, 2022. Published April 3, 2023.
Math Subject Classifications: 35Q35, 76A02.
Key Words: Capillarity; unbounded liquid bridges; uniqueness.
DOI: https://doi.org/10.58997/ejde.2023.32

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Raymond Treinen
Department of Mathematics
Texas State University
601 University Dr.
San Marcos, TX 78666, USA
email: rt30@txstate.edu

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