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Boundary behavior of capillary surfaces possibly with extremal boundary angles. (English) Zbl 1100.76016
The author studies the boundary behaviour of a capillary surface which makes a contact angle $$0$$ or $$\pi$$ with the container wall. In these cases the gradient of the graph of the capillary surface is necessarily unbounded near the boundary of the cross-section of the cylindrical container. The main result of the paper is that the solution of the associated boundary value problem is Hölder continuous up to the boundary, and that the trace of the liquid on the container wall is Lipschitz continuous, provided the solution is bounded and that the part of the boundary under consideration is in $$C^2$$. The proof relies on the special nonlinearity of the problem and, in particular, on the Stampacchia iterative procedure.
##### MSC:
 76B45 Capillarity (surface tension) for incompressible inviscid fluids 35Q72 Other PDE from mechanics (MSC2000)
##### Keywords:
regularity; Stampacchia iterative procedure
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