Ivan Blank, Alan Elcrat, Raymond Treinen
Abstract:
We present an approach to the problem of the blow up at the triple junction
of three fluids 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 finite perimeter
without making use of more advanced topics within geometric measure theory.
Specifically, using only the calculus of variations we prove two monotonicity
formulas at the triple junction for the three-fluid configuration,
and show that blow up limits exist and are always cones. We discuss some of
the geometric consequences of our results.
Submitted February 14, 2019. Published August 27, 2019.
Math Subject Classifications: 76B45, 35R35, 35B65.
Key Words: Floating drops; capillarity; regularity; blow up.
Show me the PDF file (818 KB), TEX file for this article.
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Ivan Blank Department of Mathematics Kansas State University Manhattan, KS 66506, USA email: blanki@math.ksu.edu |
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| Alan Elcrat (deceased) Department of Mathematics Wichita State University Wichita, KS 67260, USA | |
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Raymond Treinen Department of Mathematics Texas State University 601 University drive San Marcos, TX 78666, USA email: rt30@txstate.edu |
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