TY - RPRT
T1 - Where best to place a Dirichlet condition in an anisotropic membrane?
Y1 - 2014
A1 - Paolo Tilli
A1 - Davide Zucco
AB - 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.
PB - SISSA
UR - http://urania.sissa.it/xmlui/handle/1963/7481
U1 - 7592
ER -