Geometry of the triple junction between three fluids in equilibrium

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Authors
Blank, Ivan A.
Elcrat, Alan R.
Treinen, Ray
Advisors
Issue Date
2019-08-27
Type
Article
Keywords
Floating drops , Capillarity , Regularity , Blow up
Research Projects
Organizational Units
Journal Issue
Citation
Blank, Ivan A.; Elcrat, Alan R.; Treinen, Ray. 2019. Geometry of the triple junction between three fluids in equilibrium. Electronic Journal of Differential Equations, vol. 2019:art. no. 101
Abstract

We present an approach to the problem of the blow up at the triple junction of three uids in equilibrium. Although many of our results can already be found in the literature, our approach is almost self-contained and uses the theory of sets of nite perimeter without making use of more advanced topics within geometric measure theory. Specically, using only the calculus of variations we prove two monotonicity formulas at the triple junction for the three-uid conguration, and show that blow up limits exist and are always cones. We discuss some of the geometric consequences of our results.

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Description
This work is licensed under a Creative Commons Attribution 4.0 International License. This is an open access journal.
Publisher
Texas State University
Journal
Book Title
Series
Electronic Journal of Differential Equations;v.2019:art no.101
PubMed ID
DOI
ISSN
1072-6691
EISSN