01022nas a2200121 4500008004100000245005500041210005500096520063900151100002100790700002300811700001800834856004800852 2018 en d00aTransmission conditions obtained by homogenisation0 aTransmission conditions obtained by homogenisation3 aWe study the asymptotic behaviour of solutions to variational problems in perforated
domains with Neumann boundary conditions. We consider perforations that in the limit
concentrate on a smooth manifold. We characterise the limits of the solutions and show that they solve a variational problem with a transmission condition across the manifold. This is expressed through a measure on the manifold, vanishing on sets of capacity zero. Then, we prove that every such measure can be obtained by homogenising suitable perforations. Eventually, we provide an asymptotic formula for this measure by using some auxiliary minimum problems.1 aDal Maso, Gianni1 aFranzina, Giovanni1 aZucco, Davide uhttp://preprints.sissa.it/handle/1963/35310