Geometry of the triple junction between three fluids in equilibrium
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 advanc...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2019-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/101/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |