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The well-known Cahn-Hilliard equation entails mass conservation if a suitableboundary condition is prescribed. In the case when the equation is also coupledwith a dynamic boundary condition, including the Laplace-Beltrami operator onthe boundary, the total mass on the inside of the domain and its trace on theboundary should be conserved. The new issue of this paper is the setting of amass constraint on the boundary. The effect of this additional constraint isthe appearance of a Lagrange multiplier; in fact, two Lagrange multipliersarise, one for the bulk, the other for the boundary. The well-posedness of theresulting Cahn-Hilliard system with dynamic boundary condition and massconstraint on the boundary is obtained. The theory of evolution equationsgoverned by subdifferentials is exploited and a complete characterization ofthe solution is given.

Cahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundary