Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 101, pp. 1-35.

Title: Geometry of the triple junction between three fluids in equilibrium

Authors: Ivan Blank  (Kansas State Univ., Manhattan, KS, USA)
         Alan Elcrat (Wichita State Univ., Wichita, KS, USA)
         Raymond Treinen (Texas State Univ., San Marcos, TX, USA)

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.