Abstract
This paper addresses a conjecture of Concus and Finn [Capillary Wedges Revisited, SIAM J. Math. Anal., in press] on conditions for local existence of solutions of the zero-gravity capillarity equation at a boundary protruding corner pointP of prescribed opening 2α. Geometrically, surfaces of constant mean curvatureH are sought as graphs which meet vertical walls over the boundary in prescribed angles, which are locally constant except for a possible jump discontinuity atP. The conjecture is settled more or less completely in the affirmative, depending on whetherH is to be prescribed. The proof proceeds through a global existence theorem for “moon domains”, which seems of independent interest.
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