It is proved that the “bubble solutions” of the capillary equation, whose existence was shown in an earlier paper with Concus, converge, as the vertex height tends to negative infinity, to a solution of the equation which is a graph over the entire base plane with an isolated singularity. This partly settles our previous conjecture, and also provides a new and conceptually preferable proof for existence of such a singular solution. The discussion is based on a form of Green’s Identity that has an independent interest.


Singular Solution Solution Curve Pendent Drop Comparison Surface Vertical Point 
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Robert Finn
    • 1
  1. 1.Mathematics DepartmentStanford UniversityStanfordUSA

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