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On the existence of a capillary surface with prescribed contact angle. (English) Zbl 0297.76018

The existence and boundary regularity of an equilibrium free surface of a liquid that partially fills a cylindrical container, as determined by surface forces, gravitational forces and boundary adhesion, is demonstrated for cylinders of arbitrary smooth cross section. Assuming a constant “contact angle” between 0 and \(r\), we derive an a priori estimate for the tangential gradient at the boundary for solutions of the capillary equation. The case of a variable contact angle is also considered.
Reviewer: Joel Spruck

MSC:

76B99 Incompressible inviscid fluids
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