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Capillary wedges revisited. (English) Zbl 0843.76012

Summary: Equilibrium capillary surfaces in zero gravity in cylindrical containers whose sections are (wedge) domains with corners are studied. Necessary and also sufficient conditions are developed for the existence or nonexistence of surfaces that are locally graphs over the base at the corner, with (prescribed) contact angles that may differ on the two sides. It is shown that the behavior can depart in significant qualitative ways from that which occurs when the two contact angles are the same. Conditions are derived under which such qualitative changes must occur, and illustrative examples are given.

MSC:

76B45 Capillarity (surface tension) for incompressible inviscid fluids
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
49Q99 Manifolds and measure-geometric topics
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