Archivio Istituzionale della RicercaIn this paper we prove some lower bounds for the compliance functional, in terms of the 1-dimensional Hausdorff measure of the Dirichlet region and the number of its connected components. When the measure of the Dirichlet region is large, these estimates are asymptotically optimal and yield a proof of a conjecture by Buttazzo and Santambrogio.
Compliance estimates for two-dimensional problems with Dirichlet region of prescribed length / Tilli, Paolo. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - STAMPA. - 7:1(2012), pp. 127-136. [10.3934/nhm.2012.7.127]
Compliance estimates for two-dimensional problems with Dirichlet region of prescribed length
TILLI, PAOLO
2012
Abstract
In this paper we prove some lower bounds for the compliance functional, in terms of the 1-dimensional Hausdorff measure of the Dirichlet region and the number of its connected components. When the measure of the Dirichlet region is large, these estimates are asymptotically optimal and yield a proof of a conjecture by Buttazzo and Santambrogio.
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https://hdl.handle.net/11583/2498762
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