  We consider a boundary value problem for a general second order linear
equation in a domain with a fine perforation. The latter is made by small
cavities; both the shapes of the cavities and their distribution are arbitrary.
The boundaries of the cavities are subject either to a Dirichlet or a nonlinear
Robin condition. On the perforation, certain rather weak conditions are imposed
to ensure that under the homogenization we obtain a similar problem in a
non-perforated domain with an additional potential in the equation usually
called a strange term. Our main results state the convergence of the solution
of the perturbed problem to that of the homogenized one in $W_2^1$- and
$L_2$-norms uniformly in $L_2$-norm of the right hand side in the equation. The
estimates for the convergence rates are established and their order sharpness
is discussed.
