Let $\Omega_\ell = \ell\omega_1 \times \omega_2$ where $\omega_1 \subset \R^p$ and $\omega_2 \subset \R^{ n-p}$ are assumed to be open and bounded. We consider the following minimization problem: $$E_{ \Omega_\ell}(u_\ell) = \min_{ u\in W_0^{ 1,q}(\Omega_\ell)}E_{ \Omega_\ell}(u)$$ where $E_{ \Omega_\ell}(u) = \int_{ \Omega_\ell}F(\grad u)-fu$, $F$ is a convex function and $f\in L^{ q'}(\omega_2)$. We are interested in studying the asymptotic behavior of the solution $u_\ell$ as $\ell$ tends to infinity.
Categories: math.AP