Energy density for the wave equation on thin domains

In this joint work with P. Gérard, 3-d/2-d asymptotic analysis of the wave equation is undertaken for cylindrical domains with vanishing thickness. The limit equation is a 2-d wave equation but its energy density is not the weak-limit of its 3-d analogue. The computation of that limit is performed microlocally through the computation of the semi-classical measure associated to the space-time derivatives of the field.