Young Women in Harmonic Analysis and PDE

December 2-4, 2016

Jelena Jankov (J. J. Strossmayer University of Osijek)

Homogenisation of elastic plate equation

We consider a homogeneous Dirichlet boundary value problem for ${\rm{div}}{\rm{div}} (M \nabla \nabla u)=f$ which describes an elastic symmetric plate clamped at the boundary. We are interested in homogenisation of this equation. The physical idea of homogenisation is to average heterogeneous media in order to derive effective properties. Homogenisation theory is well developed for a second order elliptic equation where a key role plays H-convergence, which was introduced by Murat and Tartar (1978).