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Local and global existence criteria for capillary surfaces in wedges. (English) Zbl 0872.76017

(Author’s introduction.) This paper addresses a conjecture of P. Concus and R. Finn [SIAM J. Math. Anal. 27, No. 1, 56-69 (1996; Zbl 0843.76012)] on conditions for local existence of solutions of the zero-gravity capillarity equation at a boundary protruding corner point \(P\) of prescribed opening angle \(2\alpha\). Geometrically, surfaces of constant mean curvature \(H\) are sought as graphs which meet vertical walls over the boundary in prescribed angles, which are locally constant except for a possible jump discontinuity at \(P\). The conjecture is settled more or less completely in the affirmative manner, depending on whether \(H\) is to be prescribed. The proof proceeds through a global existence theorem for “moon domains”, which seems to be of independent interest.

MSC:

76B45 Capillarity (surface tension) for incompressible inviscid fluids
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
49Q10 Optimization of shapes other than minimal surfaces
53C80 Applications of global differential geometry to the sciences

Citations:

Zbl 0843.76012
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References:

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