Energy integral of a nonlinear traction problem in a singularly perturbed periodically perforated domain

In this paper, we consider a nonlinear traction problem for the Lam'e equations in a periodically perforated domain obtained by making in $mathbbR^n$ a periodic set of holes, each of them of size proportional to $epsilon$. Under suitable assumptions, we know that there exists a family of solutions $\u(epsilon,cdot)_epsilonin]0,epsilon_1[$ with a prescribed limiting behavior when $epsilon$ approaches $0$. Then we investigate the energy integral of $u(epsilon,cdot)$ as $epsilon$ tends to $0$, and we prove that such integral can be continued real analytically for negative values of $epsilon$.