TY - RPRT
T1 - Transmission conditions obtained by homogenisation
Y1 - 2018
A1 - Gianni Dal Maso
A1 - Giovanni Franzina
A1 - Davide Zucco
AB - We 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.
UR - http://preprints.sissa.it/handle/1963/35310
U1 - 35618
U2 - Mathematics
U4 - 1
U5 - MAT/05
ER -