Fluctuations for a conservative interface model on a wall

We consider an effective interface model on a hard wall in (1+1) dimensions, with conservation of the area between the interface and the wall. We prove that the equilibrium fluctuations of the height variable converge in law to the solution of a SPDE with reflection and conservation of the space average. The proof is based on recent results obtained with L. Ambrosio and G. Savare on stability properties of Markov processes with log-concave invariant measures.