Transmission conditions obtained by homogenisation

Given a bounded open set in [Formula presented], [Formula presented], and a sequence [Formula presented] of compact sets converging to an [Formula presented]-dimensional manifold [Formula presented], we study the asymptotic behaviour of the solutions to some minimum problems for integral functionals on [Formula presented], with Neumann boundary conditions on [Formula presented]. We prove that the limit of these solutions is a minimiser of the same functional on [Formula presented] subjected to a transmission condition on [Formula presented], which can be expressed through a measure [Formula presented] supported on [Formula presented]. The class of all measures that can be obtained in this way is characterised, and the link between the measure [Formula presented] and the sequence [Formula presented] is expressed by means of suitable local minimum problems.