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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Capillary Surfaces in Wedge Domains
Jin-Tzu Chen, Robert Finn and Erich MiersemannAbstract
We consider capillary surfaces u(x, y) in a vertical tube whose sections contain a corner (wedge) with opening 2α, 0 < 2α < 2π, and with contact angle data γ1, γ2 on the adjacent sides. We interpret geometrically and improve conditions of Lancaster and Siegel on criteria for boundedness of solutions. In the case that the solutions are unbounded we give growth estimates and in the classical case of downward gravity field a power representation asymptotic to any prescribed order. The coefficients of this expansion are independent of the particular solution considered.
- Received:
- 29.11.07
- Published:
- 29.11.07