2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72018We study the asymptotic behavior of the solution of an anisotropic, heterogeneous, linearized elasticity problem in a cylinder whose diameter $ε$ tends to zero. The cylinder is assumed to be fixed (homogeneous Dirichlet boundary condition) on the whole of one of its extremities, but only on a small part (of size $εr^ε$) of the second one; the Neumann boundary condition is assumed on the remainder of the boundary. We show that the result depends on $r^ε$, and that there are 3 critical sizes, namely $r^ε=ε^3$, $r^ε=ε$, and $r^ε=ε^{1/3}$, and in total 7 different regimes. We also prove a corrector result for each behavior of $r^ε$.Preliminary version of a Note to be published in a slightly abbreviated form in C. R. Acad. Sci. Paris, Ser. I, 338 (2004), pp. 975-980Analysis of PDEstext