%0 Report %D 2014 %T Where best to place a Dirichlet condition in an anisotropic membrane? %A Paolo Tilli %A Davide Zucco %X We 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. %I SISSA %G en_US %U http://urania.sissa.it/xmlui/handle/1963/7481 %1 7592 %$ Submitted by dzucco@sissa.it (dzucco@sissa.it) on 2014-11-07T16:09:28Z No. of bitstreams: 1 Tilli_Zucco_varifold.pdf: 379650 bytes, checksum: 341cfa2d9d25e41789652de4c99c22fe (MD5)