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Capillary surfaces in
wedge domains
Jin Tzu Chen, Robert Finn and Erich Miersemann |
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Vol. 236 (2008), No. 2, 283–305
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Abstract |
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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. |
Keywords
capillarity, mean curvature, corner behavior, comparison
method
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Mathematical Subject Classification 2000
Primary: 76B45
Secondary: 53A10, 49Q10
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Milestones
Received: 12 January 2008
Accepted: 5 March 2008
Published: 1 June 2008
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Authors |
| Jin Tzu Chen | |
| Department of Mathematics National Taiwan University Taipei, Taiwan Republic of China |
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| Robert Finn | |
| Mathematics Department Stanford University Stanford, CA 94305-2125 United States |
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| Erich Miersemann | |
| Mathematisches Institut Universität Leipzig D-04109 Leipzig Germany |
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