00995nas a2200121   4500008004300000245007400043210006900117260001000186520059200196100001700788700001800805856005000823       2014                        en_Ud  00aWhere best to place a Dirichlet condition in an anisotropic membrane?0 aWhere best to place a Dirichlet condition in an anisotropic memb  bSISSA3 aWe study a shape optimization problem for the first eigenvalue of an elliptic operator in divergence form, with non constant coefficients, over a fixed domain $\Omega$.
Dirichlet conditions are imposed along $\partial\Omega$ and, in addition, along a set $\Sigma$ of prescribed length ($1$-dimensional Hausdorff measure).
We look for the best shape and position for the supplementary Dirichlet region $\Sigma$ in order to maximize the first eigenvalue. We characterize the limit distribution of the optimal sets, as their prescribed  length tends to infinity, via $\Gamma$-convergence.1 aTilli, Paolo1 aZucco, Davide  uhttp://urania.sissa.it/xmlui/handle/1963/7481