Electron. J. Differential Equations, Vol. 2019 (2019), No. 101, pp. 1-35.

Geometry of the triple junction between three fluids in equilibrium

Ivan Blank, Alan Elcrat, Raymond Treinen

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.

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Ivan Blank
Department of Mathematics
Kansas State University
Manhattan, KS 66506, USA
email: blanki@math.ksu.edu
  Alan Elcrat (deceased)
Department of Mathematics
Wichita State University
Wichita, KS 67260, USA
Raymond Treinen
Department of Mathematics
Texas State University
601 University drive
San Marcos, TX 78666, USA
email: rt30@txstate.edu

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