  The well-known Cahn-Hilliard equation entails mass conservation if a suitable
boundary condition is prescribed. In the case when the equation is also coupled
with a dynamic boundary condition, including the Laplace-Beltrami operator on
the boundary, the total mass on the inside of the domain and its trace on the
boundary should be conserved. The new issue of this paper is the setting of a
mass constraint on the boundary. The effect of this additional constraint is
the appearance of a Lagrange multiplier; in fact, two Lagrange multipliers
arise, one for the bulk, the other for the boundary. The well-posedness of the
resulting Cahn-Hilliard system with dynamic boundary condition and mass
constraint on the boundary is obtained. The theory of evolution equations
governed by subdifferentials is exploited and a complete characterization of
the solution is given.
