Homogenization Of Biharmonic Equations In Domains Perforated With Tiny Holes

. This paper deals with the homogenization of the biharmonic equation \Delta 2 u = f in a domain containing randomly distributed tiny holes, with the Dirichlet boundary conditions. The size oe of the holes is assumed to be much smaller compared to the average distance " between any two adjacent holes. We prove that as "; oe ! 0, the solutions the biharmonic equation converges to the solution of \Delta 2 u + u = f; where depends on the shape of the holes and relative order of oe with respect to ". 1. Introduction. Let\Omega be a bounded domain in R N . For any " ? 0;\Omega " denotes a perforated domain formed by randomly removing many tiny holes (depending on ") from \Omega\Gamma Consider the biharmonic equation \Delta 2 u " = f in\Omega " ; (1.1) with the Dirichlet boundary conditions u " = @u " @n = 0 in @\Omega " "\Omega : (1.2) u " = g; @u " @n = h in @\Omega ; (1.3) We are concerned with the limiting behavior of the solution u " of problem (1.1..