SISSA Open Science

# Where best to place a Dirichlet condition in an anisotropic membrane?

 dc.contributor.author Tilli, Paolo dc.contributor.author Zucco, Davide dc.date.accessioned 2014-11-10T12:19:50Z dc.date.available 2014-11-10T12:19:50Z dc.date.issued 2014 dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/7481 dc.description.abstract 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 $\Omega$. en_US 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. dc.language.iso en_US en_US dc.publisher SISSA en_US dc.relation.ispartofseries SISSA;61/2014/MATE dc.subject first Dirichlet eigenvalue, optimization, Γ-convergence en_US dc.title Where best to place a Dirichlet condition in an anisotropic membrane? en_US dc.type Preprint en_US
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