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...
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Texas State University
2019-08-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/101/abstr.html |
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doaj-013664c372464d218f20824c08c75b022020-11-25T01:57:19ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912019-08-012019101,135Geometry of the triple junction between three fluids in equilibriumIvan Blank0Alan Elcrat1Raymond Treinen2 Kansas State Univ., Manhattan, KS, USA Wichita State Univ., Wichita, KS, USA Texas State Univ., San Marcos, TX, USA 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.http://ejde.math.txstate.edu/Volumes/2019/101/abstr.htmlFloating dropscapillarityregularityblow up |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ivan Blank Alan Elcrat Raymond Treinen |
| spellingShingle |
Ivan Blank Alan Elcrat Raymond Treinen Geometry of the triple junction between three fluids in equilibrium Electronic Journal of Differential Equations Floating drops capillarity regularity blow up |
| author_facet |
Ivan Blank Alan Elcrat Raymond Treinen |
| author_sort |
Ivan Blank |
| title |
Geometry of the triple junction between three fluids in equilibrium |
| title_short |
Geometry of the triple junction between three fluids in equilibrium |
| title_full |
Geometry of the triple junction between three fluids in equilibrium |
| title_fullStr |
Geometry of the triple junction between three fluids in equilibrium |
| title_full_unstemmed |
Geometry of the triple junction between three fluids in equilibrium |
| title_sort |
geometry of the triple junction between three fluids in equilibrium |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2019-08-01 |
| description |
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. |
| topic |
Floating drops capillarity regularity blow up |
| url |
http://ejde.math.txstate.edu/Volumes/2019/101/abstr.html |
| work_keys_str_mv |
AT ivanblank geometryofthetriplejunctionbetweenthreefluidsinequilibrium AT alanelcrat geometryofthetriplejunctionbetweenthreefluidsinequilibrium AT raymondtreinen geometryofthetriplejunctionbetweenthreefluidsinequilibrium |
| _version_ |
1724974779786592256 |