# The optimal reinforcement for a membrane and low congested regions.

## Serena Guarino Lo Bianco (Dip. Mat. e Appl. Univ. Federico II Napoli)

created by pluda on 07 Oct 2015

14 oct 2015 -- 15:30   [open in google calendar]

sala seminari, dipartimento di Pisa

Abstract.

We study how to rigidify an elastic membrane under the action of an exterior load $f$ and fixed at its boundary by adding a one-dimensional reinforcement in the most efficient way; the reinforcement is described by a one-dimensional set $S\subset\Omega$ which varies in a suitable class of admissible choices. We consider also the dual problem of a given region $\Omega$ where the traffic flows according to two regimes: in a region $C$ we have a low congestion, where in the remaining part $\Omega\setminus C$ the congestion is higher. The two congestion functions $H_1$ and $H_2$ are given, but the region $C$ has to be determined in an optimal way in order to minimize the total transportation cost.

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