Asymptotic optimal location of facilities in a competition between population and industries

Buttazzo, Giuseppe; Santambrogio, Filippo; Stepanov, Eugene

Geodesic

Parcourir par

Asymptotic optimal location of facilities in a competition between population and industries

Buttazzo, Giuseppe ; Santambrogio, Filippo ; Stepanov, Eugene

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 1, pp. 239-273

Voir la notice de l'article provenant de la source Numdam

Résumé

We consider the problem of optimally locating a given number $k$ of points in $ℝ^{n}$ for an integral cost function which takes into account two measures $ϕ^{+}$ and $ϕ^{-}$ . The points represent for example new industrial facilities that have to be located, the measure $ϕ^{+}$ representing in this case already existing industries that want to be close to the new ones, and $ϕ^{-}$ representing private citizens who want to stay far away. The asymptotic analysis as $k \to \infty$ is performed, providing the asymptotic density of optimal locations.

Publié le : 2019-02-21

MR Zbl

Classification : 49Q20, 49Q10

@article{ASNSP_2013_5_12_1_239_0,
     author = {Buttazzo, Giuseppe and Santambrogio, Filippo and Stepanov, Eugene},
     title = {Asymptotic optimal location of facilities in a competition between population and industries},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {239--273},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 12},
     number = {1},
     year = {2013},
     mrnumber = {3088443},
     zbl = {1264.49047},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_1_239_0/}
}

TY  - JOUR
AU  - Buttazzo, Giuseppe
AU  - Santambrogio, Filippo
AU  - Stepanov, Eugene
TI  - Asymptotic optimal location of facilities in a competition between population and industries
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2013
SP  - 239
EP  - 273
VL  - 12
IS  - 1
PB  - Scuola Normale Superiore, Pisa
UR  - http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_1_239_0/
LA  - en
ID  - ASNSP_2013_5_12_1_239_0
ER  -

%0 Journal Article
%A Buttazzo, Giuseppe
%A Santambrogio, Filippo
%A Stepanov, Eugene
%T Asymptotic optimal location of facilities in a competition between population and industries
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2013
%P 239-273
%V 12
%N 1
%I Scuola Normale Superiore, Pisa
%U http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_1_239_0/
%G en
%F ASNSP_2013_5_12_1_239_0

Buttazzo, Giuseppe; Santambrogio, Filippo; Stepanov, Eugene. Asymptotic optimal location of facilities in a competition between population and industries. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 1, pp. 239-273. http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_1_239_0/