A capillarity problem with mixed boundary condition

J. Serrin [8] proved that the capillarity equation with Dirichlet boundary conditions can be classically solved if a condition on the curvature of the boundary is given. We study a mixed boundary value capillarity problem. We show that the condition on the curvature of the Dirichlet boundary problem may be relaxed if we suppose that the domain is large enough. Barrier func tions are constructed by solving a new axisymmetric capillarity problem by a shooting method. The study of this problem completes the results obtained by Perko [7]. (C) 1999 Academie des Sciences / Editions scientifiques et m edicales Elsevier SAS.