Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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The optimal reinforcement for a membrane and low congested regions

Serena Guarino Lo Bianco (Università di Pisa)

created by giovanni on 08 Oct 2015
modified on 09 Oct 2015

14 oct 2015 -- 15:30

Sala Seminari (DM, Pisa)

Seminari di analisi dei dottorandi.


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 $S\subset\O$ which varies in a suitable class of admissible choices. We consider also the dual problem of a given region $\Omega$ where the traffic 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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