An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary
In this paper we analyze a mass transportation problem in a bounded domain in which there is the possibility of import/export mass across the boundary paying a tax in addition to the transport cost that is assumed to be given by the Euclidean distance. We show a general duality argument and for the...
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European Mathematical Society Publishing House
2014
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| LEADER | 05267caa a22005297a 4500 | ||
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| 001 | PAPER-14784 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518204522.0 | ||
| 008 | 190411s2014 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84894794459 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Mazón, J.M. | |
| 245 | 1 | 3 | |a An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary |
| 260 | |b European Mathematical Society Publishing House |c 2014 | ||
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Agueh, M., Existence of solutions to degenerate parabolic equations via the Monge- Kantorovich theory (2005) Adv. Differential Equations, 10 (3), pp. 309-360 | ||
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| 504 | |a Ambrosio, L., Gigli, N., Savaré, G., Gradient flows in metric spaces and in the space of probability measures (2005) Lectures in Mathematics ETH Zürich, , Birkhäuser Verlag, Basel | ||
| 504 | |a Ambrosio, L., Pratelli, A., Existence and stability results in the L1 theory of optimal transportation (2003) Optimal Transportation and Applications (Martina Franca 2001), pp. 123-160. , Springer, Berlin Lecture Notes in Math. 1813 | ||
| 504 | |a Brown, L.D., Purves, R., Measurable selections of extrema (1973) Ann. Statist., 1, pp. 902-912 | ||
| 504 | |a Caffarelli, L.A., McCann, R.J., Free boundaries in optimal transport and Monge-Ampère obstacle problems (2010) Ann. Of Math.(2), 171 (2), pp. 673-730 | ||
| 504 | |a Evans, L.C., Gangbo, W., Differential equations methods for the Monge- Kantorovich mass transfer problem (1999) Mem. Amer. Math. Soc., 137 (653), pp. 8+66 | ||
| 504 | |a Figalli, A., The optimal partial transport problem (2010) Arch. Ration. Mech. Anal., 195 (2), pp. 533-560 | ||
| 504 | |a Figalli, A., Gigli, N., A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions (2010) J. Math. Pures Appl.(9), 94 (2), pp. 107-130 | ||
| 504 | |a Kantorovich, L.V., On the translocation of masses (1942) Acad. Sci., 37, pp. 199-201. , C. R. (Doklady) URSS (N.S.) | ||
| 504 | |a Sudakov, V.N., Geometric problems in the theory of infinite-dimensional probability distributions (1976) Cover to Cover Translation of Trudy Mat. Inst. Steklov, 141 | ||
| 504 | |a Sudakov, V.N., Proc. Stekelov Inst. Math., 1979, pp. 1-178 | ||
| 504 | |a Talenti, G., Inequalities in rearrangement invariant function spaces (1994) Nonlinear Analysis, Function Spaces and Applications, 5, pp. 177-230. , (Prague 1994). Prometheus, Prague | ||
| 504 | |a Villani, C., Topics in optimal transportation (2003) Graduate Studies in Mathematics 58, , American Mathematical Society Providence, RI | ||
| 504 | |a Villani, C., Optimal transport. Old and new (2009) Fundamental Principles of Mathematical Sciences, 338. , Springer-Verlag Berlin | ||
| 520 | 3 | |a In this paper we analyze a mass transportation problem in a bounded domain in which there is the possibility of import/export mass across the boundary paying a tax in addition to the transport cost that is assumed to be given by the Euclidean distance. We show a general duality argument and for the dual problem we find a Kantorovich potential as the limit as p→∞ of solutions to p-Laplacian type problems with nonlinear boundary conditions. In addition, we show that this limit encodes all the relevant information for our problem. It provides the masses that are exported and imported from the boundary and also allows the construction of an optimal transport plan. Finally we show that the arguments can be adapted to deal with the case in which the mass that can be exported/imported is bounded by prescribed functions. © European Mathematical Society. |l eng | |
| 593 | |a Departament d'Anàlisi Matemàtica, Universitat de València, Dr. Moliner 50, 46100-Burjassot, Valencia, Spain | ||
| 593 | |a Departamento de Análisis Matemático, Universidad de Alicante, Apdo. correos 99, 03080-Alicante, Spain | ||
| 593 | |a Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a MASS TRANSPORT |
| 690 | 1 | 0 | |a MONGE-KANTOROVICH PROBLEMS |
| 690 | 1 | 0 | |a P-LAPLACIAN EQUATION |
| 700 | 1 | |a Rossi, J.D. | |
| 700 | 1 | |a Toledo, J. | |
| 773 | 0 | |d European Mathematical Society Publishing House, 2014 |g v. 30 |h pp. 277-308 |k n. 1 |p Rev. Mat. Iberoam. |x 02132230 |t Revista Matematica Iberoamericana | |
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| 856 | 4 | 0 | |u https://doi.org/10.4171/rmi/778 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_02132230_v30_n1_p277_Mazon |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02132230_v30_n1_p277_Mazon |y Registro en la Biblioteca Digital |
| 961 | |a paper_02132230_v30_n1_p277_Mazon |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 75737 | ||