  The Allen-Cahn equation, coupled with dynamic boundary conditions, has
recently received a good deal of attention. The new issue of this paper is the
setting of a rather general mass constraint which may involve either the
solution inside the domain or its trace on the boundary. The system of
nonlinear partial differential equations can be formulated as variational
inequality. The presence of the constraint in the evolution process leads to
additional terms in the equation and the boundary condition containing a
suitable Lagrange multiplier. A well-posedness result is proved for the related
initial value problem.
