  This paper concerns the theoretical and numerical analysis of a free boundary
problem for the Laplace equation, with a curvature condition on the free
boundary. This boundary is described as the graph of a function, and contact
angles are imposed at the moving contact points. The equations are set in the
framework of classical Sobolev Banach spaces, and existence and uniqueness of
the solution are proved via a fixed-point iteration, exploiting a suitably
defined lifting operator from the free boundary. The free-boundary function and
the bulk solution are approximated by piecewise linear finite elements, and the
well-posedness and convergence of the discrete problem are proved. This proof
hinges upon a stability result for the Riesz projection onto the discrete
space, which is separately proven and has an interest per se.
