Geodesic
Optimal free export/import regions
Canadian mathematical bulletin, Tome 64 (2021) no. 4, pp. 737-751

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DOI

We consider the problem of finding two free export/import sets $E^+$ and $E^-$ that minimize the total cost of some export/import transportation problem (with export/import taxes $g^\pm $), between two densities $f^+$ and $f^-$, plus penalization terms on $E^+$ and $E^-$. First, we prove the existence of such optimal sets under some assumptions on $f^\pm $ and $g^\pm $. Then we study some properties of these sets such as convexity and regularity. In particular, we show that the optimal free export (resp. import) region $E^+$ (resp. $E^-$) has a boundary of class $C^2$ as soon as $f^+$ (resp. $f^-$) is continuous and $\partial E^+$ (resp. $\partial E^-$) is $C^{2,1}$ provided that $f^+$ (resp. $f^-$) is Lipschitz.
DOI : 10.4153/S0008439520000788
Mots-clés : Shape optimization, optimal regions, import/export transport problem 
Dweik, Samer. Optimal free export/import regions. Canadian mathematical bulletin, Tome 64 (2021) no. 4, pp. 737-751. doi: 10.4153/S0008439520000788
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     title = {Optimal free export/import regions},
     journal = {Canadian mathematical bulletin},
     pages = {737--751},
     year = {2021},
     volume = {64},
     number = {4},
     doi = {10.4153/S0008439520000788},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000788/}
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