### $\text{\Gamma}$-convergence for a class of functionals with deviating argument.

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In the paper the problem of constructing an optimal urban transportation network in a city with given densities of population and of workplaces is studied. The network is modeled by a closed connected set of assigned length, while the optimality condition consists in minimizing the Monge-Kantorovich functional representing the total transportation cost. The cost of trasporting a unit mass between two points is assumed to be proportional to the distance between them when the transportation is carried...

Given the probability measure $\nu $ over the given region $\Omega \subset {\mathbb{R}}^{n}$, we consider the optimal location of a set $\Sigma $ composed by $n$ points in $\Omega $ in order to minimize the average distance $\Sigma \mapsto {\int}_{\Omega}\mathrm{dist}(x,\Sigma )\phantom{\rule{0.166667em}{0ex}}\mathrm{d}\nu $ (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all $n$ points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving...

Given the probability measure over the given region $\Omega \subset {\mathbb{R}}^{n}$, we consider the optimal location of a set composed by points in in order to minimize the average distance $\Sigma \mapsto {\int}_{\Omega}\mathrm{dist}\phantom{\rule{0.166667em}{0ex}}(x,\Sigma )\phantom{\rule{0.166667em}{0ex}}\mathrm{d}\nu $ (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving the...

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